Modeling STM tips by single absorbed atoms on W(100) films: 5d transition metal atoms.

Transcription

1 Modeling STM tips by single absorbed atoms on W(100) films: 5d transition metal atoms. W. A. Hofer, 1 J. Redinger Institut für Technische Elektrochemie und Festkörperchemie and Center for Computational Material Sciences, Technische Universität Wien, Getreidemarkt 9/158, A 1060 Wien, Austria P. Varga Institut für Allgemeine Physik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria Abstract The apex atom plays a key role in STM tunneling, in particular if subtle effects like atomic and chemical resolution on metal alloys are considered. In order to provide comprehensive data on the electronic structure of realistic tips we have calculated tungsten (100) films with single apex atoms by first principles molecular dynamics and full potential methods. Molecular dynamics using ultrasoft pseudo potentials has been used to determine the relaxation of the surface layers. The electronic structure of the relaxed film has been calculated with a first principles full potential method, which is most suitable to reproduce the subtle surface effects due to alloying. The results suggest that a correct result for the current and corrugation values in the perturbation approach can only be obtained by including the full electronic structure of the tip. Keywords: A. metal C. scanning tunneling microscopy D. tunneling 1 Introduction It has long been suspected that the contamination of a scanning tunneling microscope (STM) tip with single atoms of the sample surface or adsorbates may play a key role in STM imaging. However, till recently the theoretical models to describe the tunneling process were either restricted by too low 1 address: whofer@cms.tuwien.ac.at Preprint submitted to Elsevier Science 1 October 1999

2 computer efficiency and thus not very well founded approximations of the interactions, or they used, e.g. in the Tersoff-Hamann model [1], rather simple models of the STM tip. The first step towards more realistic models of the tip was due to Chen [2], who demonstrated the effect of p and d-like tip states on the corrugation of sample surfaces. With the present increase of computer performance the simulation of currents in an STM seems finally tractable also in day to day evaluations of tunneling measurements. Such an improved model may lead to a better understanding of the images, and it may also set the claim of tip contaminations on a more solid basis. In particular we shall demonstrate that the electronic structure of a realistic tip is determined by the mixture of s, p and d states, and that, contrary to frequent assumptions, the density of states around the Fermi level is not constant, but highly dependent on the energy and the contaminant atom. From a theoretical point of view there exists a wealth of different methods, the most important ones centered around a scattering approach and, generally, the Lippmann-Schwinger equation [3], while the assumption of non-interaction between the STM tip and the sample surface is the basis for a time dependent perturbation approach, which leads, in general, to the formulation of a Bardeen like integral [4]. Whether one or the other approach is more suitable, depends on the focus of interest and on the systems treated. It can be shown, for example, that most effects on metal surfaces are sufficiently well described if only the electronic structure of the sample is considered [5 7], while single absorbed molecules on a substrate are simulated in good agreement with experiments in a scattering approach, where the substrate is described by a tight binding model [8]. To a certain extent the history of development also seems to play a role in these preferences, since most codes were developed as an extension to existing methods. Recent results on binary alloy surfaces, based on full potential density functional calculations of films and a numerical evaluation of the Bardeen integral suggest that the apex atom of the STM tip is of key importance in the imaging process of binary alloys, since experiments and simulations are only in agreement with specific apex atoms, while they disagree with others [9]. That the tip atom may substantially change the result of an STM scan has already been shown by Tersoff and Lang in their simulation of a graphite surface [10]. Judging from these result it seems mandatory, if a method based on the Bardeen integral is applied, to consider all possible apex atoms in a given experiment. In this case the structure of the tip, which is not too well known in most experiments (notable exceptions are a recent work by Cerda et al. [8], or the attempt by Vazquez de Parga et. al. [11] to refer tunneling spectroscopies on Cu(111) to different surfaces of the STM tip, as well as the older work by Tersoff and Lang [10]), can be determined, even possible obstacles to good quality images of a surface (e.g. contamination of the tip). 2

3 In this paper we present first principles simulations of bcc tungsten films with single apex atoms, the apex atoms are of the 5d transition metal group, we restrict our analysis to the relevant elements of the group, i.e. W, Re, Os, Ir, Pt, and Au. The aim of this analysis is to provide a fairly complete picture of the trends concerning the electronic structure of tungsten tips contaminated by a 5d transition metal atom. The chemical nature of the apex atom is relevant for the composition and vacuum decay of the wavefunctions of the tip, in the Bardeen formulation a decisive measure for the tunnel current between tip and sample. To simulate therefore a realistic tip the apex has to be monoatomic, which requires a separation of surface atoms of at least two lattice constants. This, theoretical, requirement suggested to use the bcc (100) surface as the basis of our tungsten film calculations. 2 Method The results presented were computed with two different first principles DFT methods. In order to exclude coupling between adjacent surface atoms, which would change the features of the wave functions above the surface, the setup of the tungsten film was chosen in such a way, that the separation between the apex atoms is at least two lattice constants or 6.38 Å. For the relaxation of the apex atom and the surface layer we used a pseudopotential molecular dynamics code, the Vienna ab initio simulation program (VASP) [12,13]. The exchange correlation was the GGA according to Perdew et al. [14]. As Methfessel, Henning and Scheffler established 1992 [15], relaxations depend critically on the crystal lattice constant. We therefore used the theoretical GGA lattice constant of 3.19 Å [16] for the determination of relaxation effects. The integration of the Brillouin zone was performed with 3 k-points in the irreducible wedge. The equilibrium positions of the ions were the input geometry of a full potential augmented plane wave (FLAPW) calculation of the surface electronic structure, as the FLAPW is still the most suitable technique to simulate transition metal surfaces due to its special film geometry and its advantages as an all-electron method [17]. In this part of the calculation we integrated the Brillouin zone with ten special k-points in the irreducible wedge. The setup has been used in previous calculations [19], a sketch is shown in Fig. 1. In order to compare the DOS of different apex atoms we used one and the same muffin tin radius for all calculations. 3

4 3 Relaxation, workfunction, and magnetic moments Relaxation of the apex atom is in every case substantial and depends very much on the chemical nature of the apex. For most elements we find an inward relaxation of more than 10 % (with respect to the unrelaxed interlayer distance of 1.59 Å), the relaxation is a maximum for Osmium (21.2 %), followed by Iridium (20.9 %) and Rhenium (18.8 %). The trends exhibit a parabolic variation with the valence, which bears on the trends in the cohesive energies of the 5d elements, manifest e.g. in the surface energy calculations of Skriver and Rosengaard [18]. All surface atoms, are relaxed inward with the notable exception of Au, which is relaxed outward by 8.9 %. In our view the latter result should have an experimental consequence, i.e. that due to the weak bonding of an Au atom to the tungsten surface this tip should in general not be stable. The surface layer is relaxed inward by about 6-10 %, relaxation of this layer is fairly independent of the apex for the the elements of our series, the highest inward relaxation of 9.0 % and 10.3 % is found for Pt and Au apex atoms, respectively. The results are in the range of values found by Methfessel for the surface relaxation of W(100) using a full potential tight-binding code (- 8.3 % [15]). Regarding magnetic properties of single 5d atoms [20] we found that the high inward relaxation, especially for the elements in the middle of the series, effectively quenches the moments due to d d band interactions: the apex atom in every case has zero magnetic moment. The results of surface relaxations are displayed in Table 1. The workfunction of a bcc W(100) crystal is about 4.4 ev [21], due to the missing atoms in the surface layer it is reduced for the film with a single apex: we calculated 3.64 ev for a tungsten apex, which is slightly lower than the value found in previous calculations using the local density approximation (LDA) of 3.74 ev. The change is mainly due to an increase by about 50 % of the inward relaxation in the GGA calculation, which shows a larger lateral lattice spacing (a GGA > a LDA ). The trend in the workfunctions reflects, again, the chemical nature of the apex. The value is lowest for a tungsten apex (3.64 ev), increases to 4.04, 4.35 and 4.65 ev for rhenium, iridium and osmium, has its peak with a platinum apex atom at 4.91 ev, and drops again to 4.68 for Au. A similar trend for the close packed surfaces of the metal elements have been obtained by Skriver and Rosengaard, which can be seen as a result of the d-bonds between nearest neighbors. Workfunctions are given in Table 1. 4 Density of states The states of the tip contributing to the tunnel current have been of primary interest ever since Chen claimed that only the high contribution of d-like states 4

5 can account for the experimentally observed atomic resolution of an STM [22]. The claim was substantiated by cluster calculations of Ohnishi and Tsukada [23], where these authors established that (i) the states at the Fermi level are mainly d-like states, and that (ii) these states contribute more than 90 % to the tunnel current in the low bias regime. However, given a recent paper by de Parga et al. [11], where those authors claim that the states responsible for the tunnel current in Cu(111) spectroscopies are mainly s-like states and that the density of states of these states is fairly constant in a wide energy range for a bcc tungsten slab, the matter seems far from being settled. We wish to add some new features to the picture by an analysis of the density of states (DOS) at the apex atoms as well as in the vacuum range above the surface. The DOS was computed by a triangular mesh of 20 k-points for the IBZ, we calculated the DOS in three equally spaced slices at at 1, 2, and 3 Åabove the vacuum boundary. The DOS was smoothed with a Gaussian of 0.1 ev (FWHM). In general the features of the vacuum DOS do not change significantly for larger vertical distances above the surface, all that can be usually observed is an exponential decay which originates from the exponential decay of the vacuum wavefunction, a feature inherent to the FLAPW method. For this reason only the first interval is displayed. Since it is especially enlightening to consider the transition from the surface atoms, where one angular momentum dominates, to the vacuum, where only the the mixture of angular momenta is accessible, we show the s, p and d contributions in the surface atoms together with the DOS in the first vacuum layer. There is some evidence that a tungsten apex might be rarely present in experimental situations, which could be further substantiated for the chemical contrast of binary alloys [9]. From the experimental point of view the results on binary alloys are obtained at the lower limit of tip and sample separation, which means at a low bias voltage and they are obtained at rather high currents. In this regime the tunnel current is determined primarily by states at the Fermi edge of the STM tip. The solid black line gives the DOS integrated over the apex atom shown in Fig. 2. Analyzing the DOS it can be said that it shows a rather low value (a total of 0.42 states/ev) at the Fermi level, while the DOS structure is dominated by two peaks below and above the Fermi level at and ev, respectively. An additional minor peak exists at ev. For topographic images all three peaks are too far from the Fermi level to contribute to the tunnel current. However, in spectroscopic mode the same does not hold and the tunnel current in a spectroscopy should reflect the electronic structure to a certain extent. If the spectrum is analyzed in view of the angular momentum of the eigenfunctions, it can be seen that most of the contributions originate in the d-band, while the p-band becomes important only in the range above 0.5 ev. It is usually argued that d states have a rather large decay length and that therefore the wavefunctions in the vacuum region only matter if they possess s and p symmetry. This argument is not completely correct, when single contributions are considered. In the occupied 5

6 range of eigenvalues up to ev the grey curve, showing the DOS at 1 Å above the vacuum boundary (in STM scans the wavefunctions in this range determine the current at a core-core distance of about 5 Å) remains close to the respective s and p values. From this result the effect of different bias voltages may be deduced. In case of tunneling from tip to sample (positive bias voltage and negative energy difference between the two Fermi levels) the initial states are mostly s and p. At a low positive bias voltage of less than 0.2 ev d states of the tip start to play a more important role, they dominate the negative bias range to about -1V, and in the lowest range below - 1V the final states are again p states. A W terminated tip thus shows an intricate balance between states of different angular momentum possessing different decay lengths into the vacuum range. Since in most models, where the tip is simulated by a single state, it is assumed, that in the Bardeen integral I ev 0 ρ S (E F ev + ǫ)ρ T (E F + ǫ) M 2 dǫ (1) ρ T (E F + ǫ), the DOS of the tip remains constant near the Fermi level, these models are subject to systematic errors due to the structure of the DOS in realistic tips. Due to its high resistivity to poisoning rhenium is used as a catalyst in a few critical fields of application (e.g. hydrogenation). The structure of the Re apex atom DOS is similar to the previous one, with some shifting of the maxima and minor changes, though. The two maxima in apex are at ev and ev relative to the Fermi edge, the maximum just below the Fermi level is shifted to ev and the peak is substantially broadened. This peak is due to additional d states in the DOS, which also show up in the vacuum as a distinct peak. Directly at the Fermi edge the DOS is higher (0.7 states/ev) than previously, also in this case we have a high contribution of d states which protrude into the vacuum. The maximum of the DOS in the vacuum is at 0.34 ev, and contrary to the previous case also the states above 1 ev have a substantial contribution with d-like symmetry. Apart from this change spectroscopies should encounter similar features of the tip: a dominating s and p band in the low range of occupied states, increased contributions of the d band slightly below the Fermi edge with one distinct maximum, and a mixture of p and d states in the positive energy regime, corresponding to negative bias voltages. Osmium, like rhenium, is used in catalysts for industrial applications. The Os apex atom has the largest inward relaxation of the elements considered (see the previous sections), its DOS exhibits a distinct maximum near the Fermi level at ev (apex atom) and 0.16 ev (vacuum). In contrast to W and Re the states in the apex atom are, over the whole energy range, primarily d-states, with a non-vanishing contribution of p-states only at the Fermi level. 6

7 The s-states are negligible over the whole range. The dominance of d-states entails a significant contribution of these states in the vacuum region, which is verified only for positive energies (from ev to 2 ev), while for energies below ev the d-states possess a very short decay length and the vacuum DOS remains close to the DOS of the p band. For STM topographies the simulations suggest a high influence of p and d tip-states (the broad peak in the vacuum DOS has a maximum of 0.70 states/ev, the main contributions should be from the p and d like states), since the inward relaxation is very high, a Os terminated tip should also be very stable. For spectroscopies the picture is less clear and similar to the Re tip: a prevailing p symmetry of relevant tip states in the negative energy range and a mixture of p and d in the positive range without substantial contributions from the s-band. Iridium is one of the hardest and the most corrosion resistant metal known. Like the Os apex, the Ir atom is relaxed inward by more than 20 % (interlayer distance of ideal bulk). The dominant peak in the atom DOS, which is clearly above the Fermi level for W and Re, is at the Fermi edge for Os and Ir, with a slight downward shift (maximum at 0.00 ev). The DOS at this level is composed of 15 % p states and 84 % d states, while s contributions are less than 1 %. A second maximum in the positive energy range gives an even higher contribution from the d band (89 %). The general trend in the vacuum is a fast decay of d states for energies not in the vicinity of the Fermi level, which means that spectroscopies should reveal tunneling primarily via p states of the STM tip. Near the Fermi level the d states prevail also in the vacuum region, in this energy range, commonly active in topographic studies of a surface, the simulations predict a composition of p and d states for the relevant tip orbitals. Also in this case s states seem insignificant. Platinum is widely used in industrial and non-industrial applications, and a wide range of STM studies of Pt-based surfaces, regarding electronic properties, chemisorption, catalytic processes etc. is available in the literature [25]. In particular it was proposed that Pt contamination of a tungsten tip could be responsible for the enhanced chemical contrast observed on PtCo(100) [9]. When the DOS in the vacuum range is analyzed, the reason for this enhancement is easily detected: the vacuum DOS corresponds, over the whole energy range, roughly to the DOS of p states in the apex atom. And it has been established by Chen [24] that p states, via the derivative rule, lead to an enhancement of corrugation. It should be noted that the maxima of the DOS in the Pt atom are generally lower than in the previous cases and that their position is shifted towards the negative end of the spectrum. Two distinct maxima exist at 0.82 ev, in the negative range the maxima occur at ev and ev. In all cases the maxima of the d band coincide with p-band maxima. The general trend for STM measurements in case of Pt contamination of the tip is a high contribution of p states, fast decay of relevant d states and low contribution of these states in the tunneling process, and a negligible contribution of s states. 7

8 As already mentioned in the discussion of relaxation effects, the high outward relaxation suggests that an Au contamination of the STM tip is a rather unlikely case. However, for the sake of completeness, and since Au clusters on surfaces play a role in industrial applications and are therefore also a topic of research, we present here the DOS in the Au atom and in the vacuum region above the surface. The DOS of the apex atom displays two peaks in the negative energy range, at ev and ev, respectively. In the vacuum the DOS coincides with the p states in the atomic spheres, vacuum states are therefore predominantly p states. The maxima and minima of the DOS in the vacuum range are, apart from a sharp maximum at ev and which is due to a slight contribution of d states, not very prominent. A spectroscopy with a Au terminated tip should thus reveal the electronic structure of the sample rather than any structure of the tip. 5 Conclusion We have presented a first principles study modeling the electronic structure of an STM tip by a tungsten film with single adsorbed 5d transition metal atoms. In all cases we found a dominance of d states in the apex atom for the energy range considered (- 2 ev to + 2 ev). In contrast to the composition of states in the apex atom the composition in the vacuum range above the sample surface depends on the energy interval considered as well as the element. It was shown that the negative energy range in the vacuum is dominated by p states, the Fermi level by a substantial contribution of d-states, while the positive energy range of the tip is composed of p and d states, depending on the element. In all cases the contributions of the s band were fairly insignificant. The result suggests that STM tips contaminated with a 5d transition metal atom will measure currents and corrugations which deviate from the usual results calculated with the Tersoff-Hamann model. The exact values, thus the conclusion also within the perturbation approach, have to be calculated by computing the Bardeen integral. Acknowledgements This work was supported by the Austrian Science Foundation under Project Nos S8103-PHY and S8106-PHY, and the Center for Computational Materials Science, Vienna, Austria. Thanks are also due to Georg Kresse, who helped us overcome the activation barriere as VASP users. 8

9 References [1] J. Tersoff and D. R. Hamann, Phys. Rev. B 31, 1985, 805. [2] J. C. Chen, Phys. Rev. Lett. 65, 1990, 448. [3] B. A. Lippmann and J. Schwinger, Phys. Rev. 50, 1950, 469. [4] J. Bardeen, Phys. Rev. Lett. 6, 1961, 57. [5] A. Biedermann, O. Genser, W. Hebenstreit, M. Schmid, J. Redinger, R. Podloucky, P. Varga, Phys. Rev. Lett. 76, 1996, [6] W. A. Hofer, G. Ritz, W. Hebenstreit, M. Schmid, P. Varga, J. Redinger, R. Podloucky, Surf. Sci. Lett. 405, 1998, L514. [7] S. Heinze, S. Blügel, R. Pascal, M. Bode, R. Wiesendanger, Phys. Rev. B 58, 1998, [8] J. Cerda, M. A. van Hove, P. Sautet, M. Salmeron, Phys. Rev. B 56, 1997, and [9] W. A. Hofer and J. Redinger, Scanning tunneling microscopy of binary alloys: first principles calculation of the current for PtX (100) surfaces, Surf. Sci., 1999, in press [10] J. Tersoff and N. D. Lang, Phys. Rev. Lett. 65, 1990, [11] A. L. Vasquez de Parga, O. S. Hernan, R. Miranda, A. Levy Yeyati, N. Mingo, A. Martin-Rodero, F. Flores, Phys. Rev. Lett. 80, 1998, 357. [12] G. Kresse and J. Hafner, Phys. Rev. B 47, 1993, 558. [13] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 1996, [14] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pedersen, D. J. Singh, and C. Fiolhais, Phys. Rev. B 46, 1992, [15] M. Methfessel, D. Hennig, and M. Scheffler, Phys. Rev. B 46, 1992, [16] G. Kresse, private communication [17] E. Wimmer, H. Krakauer, A. J. Freeman, Adv. Electron. Electron Phys. 65, 1985, 357. [18] H. L. Skriver and N. M. Rosengaard, Phys. Rev. B 46, 1992, [19] W. A. Hofer and J. Redinger, Phil. Mag. B 78, 1998, 519. [20] V. S. Stepanyuk, W. Hergert, K. Wildberger, R. Zeller, and P. H. Dederichs, Phys. Rev. B 53, 2121 (1996) [21] C. L. Fu, S. Ohnishi, H. J. F. Jansen and A. J. Freeman, Phys. Rev. B 31, 1985,

10 [22] C. J. Chen, Phys. Rev. B 42, 1990, [23] M. Tsukada, K. Kobayashi, and N. Isshiki, Surf. Sci. 242, 1990, 12. [24] J. J. Chen, Introduction to Scanning Tunneling Microscopy, Oxford Univ. Press, Oxford [25] P. Varga and M. Schmid, Appl. Surf. Sci. 141, 1990,