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Unoccupied electronic band structure effects in low-energy SEES and TCS of some d-metals
Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 11–16 www.elsevier.com / locate / elspec
Unoccupied electronic band structure effects in low-energy SEES and TCS of some d-metals O.F. Panchenko* A. A. Galkin Donetsk Institute of Physics and Technology, Ukrainian National Academy of Sciences, 72 Rozy Luxemburg Street, 83114 Donetsk, Ukraine
Abstract The fine structure of the experimental secondary electron emission spectra (SEES) along the normal to a Ir(111) surface and the target (total) current spectra (TCS) along the normal to a Cu(111) surface are interpreted theoretically. It is shown that the fine structure of SEES and TCS is mainly due to the electronic structure of unoccupied high-level electronic states (above the vacuum level Evac ) to which the electrons come or from which they emit. The predominant role of the effects of bulk energy-band structure in the formation of spectra is shown. Comparison to existing experimental data is given. 2002 Elsevier Science B.V. All rights reserved. Keywords: Low-energy electrons; Secondary electron emission spectra; Target (total) current spectra; Fine structure; Band structure; d-Metals
1. Introduction The electronic band structure (BS) is a fundamental characteristic that predetermines a majority of solid state features [for example, transfer phenomena, optical and photoemission (PES) features]. It is also one of the major factors in determining the functioning of solid state electronic devices. The traditional research methods as regards the unoccupied high-level electronic states are: X-ray absorption spectroscopy (XAS) [1], bremsstrahlung isochromat spectroscopy (BIS) [2], inverse PES (IPES) [3], very low-energy electron diffraction (VLEED) [4], and low-energy secondary electron spectroscopy. The latter is characterized by the high surface sensitivity and the absence of destructive impact on an investigated sample. The secondary electron *Tel.: 1380-622-553-585. E-mail address: [email protected] (O.F. Panchenko).
spectroscopy, based on the study of phenomena accompanying the process of interaction between the flow of slow-moving primary electrons (PEs) Ip (with energy Ep #1 keV) and crystal surface, consists of two methods [5,6]: differential and integral ones. The former gives the distribution curve by the energy of secondary electrons (SEs) outside the crystal or secondary electron emission spectra (SEES). The latter gives the curve of the integrated (or total) current of SEs in the sample or target (total) current spectra (TCS). The main features of the fine structure (FS) of SEES and TCS, showing the whole complex of phenomena taking place in the near-surface layer, are mainly connected with the bulk BS of the crystal [7,8]. SE-emission of metals has been experimentally investigated by many authors; in most cases the objects of investigation were polycrystals. The FS at the background of SEES cascade maximum (CM) was, for example, observed in the energy distribution
0368-2048 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 02 )00167-6
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of SEs of the Ir [9], Pt [10], Ag [11–13], Si [14–16], W [7,17–21], Pd [22,23], Ni [24,25], Fe [26,27], Cu [28–30], and Al [31] single crystals. The theoretical analysis of SEES turned out to be rather difficult because it was necessary to take into consideration all the physical processes taking place at the interaction of PEs flow with the crystal. The experimentally observed FS of SEES could not be explained by the theories within the model of free electrons without taking account of the BS. Calculations of the SEES done in Ref. [7] have shown how the FS relates to the bulk density of states r (E); there only the spectral line position (but not shape and intensity) has been analysed with neglect of the energy level broadening. The FS of SEES has been interpreted in Refs. [13,17,30,32] basing on the theory of LEED. The results of Ref. [17] differ from those of Refs. [7,32] though they satisfactorily describe the FS of the experimental curves. In Ref. [9] the experimental angle-resolved SEES are interpreted as emission from excited bulk bands (some additional features are interpreted as surface resonances) without any theoretical calculations. In so doing, the BS E(k) of the conduction band is calculated by construction of energy Ei of the spectrum peaks as the function of angle emission k. In Refs. [15,18,33,34] it is shown that the FS of SEES is determined by the energy dispersion of unoccupied high-level electronic states and represent the boundaries of bands in the dispersion of electrons moving in direction of detection. A comparatively small number of papers (see, e.g., Refs. [6,8,12,35–42]) has been devoted to the investigation of the TCS—the derivative with respect to Ep from total current in circuit of a sample I5Ip 2Is , where Is is the current of electrons, both elastically (including the intensity of specularly reflected elastic beam I00 measuring in the LEED experiments) and inelastically reflected, emitted from the sample. According to Refs. [6,12,35,36], in the energy range to 100 eV the electron–electron (e–e) scattering with the excitation of interband transitions prevails, and the main structures in the TCS represent the peculiarities of r (E). A relation between the FS of TCS and the bulk BS is also confirmed by calculations done in Refs. [37,39,40,43] by using the LEED theory. The aim of this paper is to elucidate the reg-
ularities of SEES and TCS FS formation, their relation with the bulk BS and to develop a technique for the processing of experimental results to obtain the maximum of information on the electron dispersion above Evac . As before (see, e.g., Refs. [15,18,44,45]) during the calculation of the Ir(111) SEES and the Cu(111) TCS the electron scattering with a preset momentum at the crystal was considered within the approximation, when the probability of scattering was proportional to a number of finite states at a given level of energy E with a preset direction of quasi-momentum V. The energy dependence of the band energy level broadening "G (E) 5 " /t (E), the e–e and electron–plasmon contribution to the nonequilibrium SEs-distribution function f(E), the isotropic component of current from the electrons scattered on the surface were taken into consideration. The paper is based on real BS Enk and r (E) [46–48]. Enk enters the calculations of spectra through N(E,V ) (see, e.g., Fig. 1a) is the number of the energy bands along direction V, for which the equality E5Enk is satisfied. As to the taking into consideration the surface effects which contribute to the formation of N(E,V ), the following can be said. The specific features of the electronic spectrum of metal surface are connected with the fact that the electronic spectrum, typical of the bulk, is not practically disturbed in the near-surface region, and the local surface states appear only on its background. This is confirmed by the data of numerous PES investigations (see, for example, Refs. [49,50]). The geometric structure of surface lattices of atomicpure metal surfaces does not, as a rule, differ from the structure of the bulk.
2. Results of the SEES calculation Fig. 1b shows the results of SEES calculation along the normal to a Ir(111) surface with the attraction of the bulk BS obtained by different authors. The background component of current—a structureless CM (peak A in Fig. 1) was taken into account by the addition of constant C to N(E,V ) when the electronic structure of the near-surface region is described by a model of nearly free electron gas. As is shown in Ref. [15], the varying of C in a
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Fig. 1. (a) A number of Ir electron dispersion branches [46] (L6 1 , L6 2 , G6 2 , G7 2 , G8 2 its points of symmetry) that intersect the level E along the direction V ; (b) the SEES along the normal to a (111) surface: (1) experiment (from Ref. [9] for the G LW azimuth) for Ep 540 eV; (2) theory based on BS calculations [46] at Epl 50.96 eV; (3)–(5) theory based on BS calculations [46–48], respectively, at Epl 50.27 eV. Curves 1–5 are plotted on the ordinate arbitrarily. The energy E refers to Evac . Vertical dotted lines with the lettering A–D show the main singularities of the experimental SEES.
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wide limit from 0 to 100 does not practically change the type of second derivative J0(E,V ) which is explained by a small dependence of J0(E,V ) on the background component for all E, except for the neighborhood of CM. For J(E,V ) calculation the following values of parameters have been used: C5 4 (gives CM shape and width close to the experiment); Evac 5EF 1ew, where EF 510.8 eV and ew 5 5.8 eV. A range of parameters used in our calculations does not significantly influence the final results. The work function ew determines only the initial energy reading both for SEES along the normal to a Ir(111) surface and for TCS (see below) along the normal to a Cu(111) surface. We refer to ew as a parameter because there exist certain variations in how to determine its value. For example, according to the reference data for Ir(111): ew 55.7460.06 eV and ew 55.860.03 eV (method of thermoelectron emission); ew 55.7960.03 eV (method of surface ionization of atoms). It is obvious that our chosen value ew conforms well, within the tolerance limits of the measurements, to these data. Similarly, we used ew 54.2 eV for Cu(111) (according to Ref. [6]). The Fermi level EF was selected from the calculations of the BS used by us [46–48]. Thus, for Ir: EF 510.8 eV (according to Ref. [46]), EF 510.76 eV [48], and EF |11 eV [47]; for Cu: EF 59.2 eV [47]. The variation of the EF value within 0.2 eV does not significantly influence the final result which is of qualitative rather than quantitative nature. It also correct because, besides the error of our calculations, there exists the error (#0.5 eV) for experimental curves which we have provided so that you could use them as a base for comparison with our calculations. The lifetime of the excited state t (E) was determined from Ref. [51]: " /t (E)5Epl (E /EF 21)2 , where Epl is the screening parameter. The occupation states function f(E), responding to the multiple e–e scattering, has been obtained in Ref. [52] at E2EF , ,Ep by solving a system of transport equations within the approximation of e–e scattering statistical model. This system describes the cascade process of the inelastic scattering of the PEs flow. The decay of plasmons, generated by the PEs as well as by the excited electrons in a solid, contributes to f(E) which, when neglecting the plasmon dispersion, has been obtained from the energy conservation law [52].
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Curve 3 the best agrees with the FS (peaks B, C and D) of experimental spectrum [9] (curve 1), when the parameter of broadening Epl , depending on concentration of s- and d-electrons in the electronic shell of an atom, was calculated starting not from the general theory of metals (as for curve 2) but was a fitted one. This is because t (E), responsible for peak broadening and used in calculations, has been obtained in Ref. [51] near the Fermi surface and not in the region of high-lying excited states. Position and intensity of the FS maxima C and D on curve 4 are essentially different from analogous peculiarities of the experimental spectrum which is because of the approximate calculations of the BS [47] within the RAPW method for E $15 eV above EF . With the BS calculation [48] within the RKKR method, to identify the FS of the experimental spectrum (see curve 5) was not a success. As is seen from Fig. 1, the jumps of the function N(E,V ) correspond to extreme values of J(E,V ). These jumps or thresholds are formed at boundaries of bands of the resolved energy values for each of the energy bands. Presence of large background component in the Ir(111) SEES in the neighborhood of CM (Fig. 1, curve 1) disables one to distinguish between the bulk and surface effects in the spectrum ha similar situation was observed by us in Ref. [34] during the interpretation of the Ge(111) SEESj. As is shown in Refs. [15,25], the double differentiation of the spectrum could eliminate these difficulties. Apart from this, separation of the bulk and surface properties is also possible when investigating the SEES under the absorption of dissimilar particles [9,10,20,22,53–55]. And the change of FS features serves a measure of the presence of defects in the near-surface layer of the sample, which can be successfully used to control surface states during the processing.
3. Results of the TCS calculation The results of the TCS S(E,V ) calculation (Epl 54 eV) are shown in Fig. 2 (curves 3, 4) for Cu(111). In Fig. 2 (curves 1, 2, 5 and dashed curve) the experimental TCS [4,6,37,39] are shown for comparison. The spectra have the FS which is essentially dependent on single-crystal orientation. The intensity
Fig. 2. TCS along the normal to a Cu(111) surface: (1), (2) the experimental results dI(E,V ) / dE from Refs. [6,39], respectively hdashed curve represents the TCS data dI(E,V ) / dE from Ref. [4] on the unrelaxed (111) surfacej; (3) theory dI(E,V ) / dE; (4) theory d 2 I(E,V ) / dE 2 ; (5) experiment d 2 I(E,V ) / dE 2 from Ref. [37]. Curves 1–5 are plotted on the ordinate arbitrarily. The energy E refers to Evac . The positions of TCS typical maxima are denoted by a, b, c, . . . , f 9 in increasing energy.
of FS|1% of the value of PEs-distribution maximum (in figures it is absent), which occurs at the energy when the electrons start hitting the sample. The main peculiarities of the Cu(111) TCS (the maxima c–g) are in agreement with the representations on the bulk BS in the near-surface region. On the background of spectrum structure corresponding to the bulk (discussed in Ref. [44]), the maxima a, b (curve 1) and b9 (curve 5) are observed, the formation of which is connected with the excitation of electrons from the occupied states located near EF . These states are the
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surface ones, they develop only in the experiments [6,37] and are not registered in the experiments [4,39], and are absent on the theoretical curves, constructed without considering both elastic scattering and the surface structure and states. Differences in the position of singularities on theoretical and experimental curves are connected (as was stated above) on one hand, with the approximate character of BS calculation for high-lying levels [47] (according to Ref. [4], the unoccupied high-level electronic states, contrary to the universally accepted point of view, can be characterised by considerable deviations from the free electron dispersion, and influenced by multi-electronic effects). On the other hand, there exist the experimental errors connected with the formation of collimated electron beam in the region of low energies, realization of the total collection of SEs, etc. Thus, the energy position and the intensity of maxima in the TCS of Cu(111) highly depend on the angle of primary beam incidence [4,35]. Singularity d (curve 1) abruptly decreases when the electron beam deviates from the normal to the surface. In the experiment this fact was used as a criterion of conditions for the normal incidence of primary beam. Singularities a, b and b9 can be explained by both the high surface sensitivity of the TCS determined not only by a small depth of the analysed region, but by a high dependence on the physical and chemical surface processes [36,38], and the deviation of the electron beam from the normal, with some error in the orientation of faces. Note that the absorption of residual gases (|10 22 Pa) on a Cu(111) surface or the ionic bombardment thereof also results in maxima a and b vanishing; subsequent desorption of residual gases is accompanied by the restoration of their intensity [6]. The absorbents or dissimilar atoms and defects present on the surface result in the large-angle elastic scattering, thus opening new channels for the electron penetration to the crystal.
4. Conclusion The obtained correspondence between the main features of experimental and theoretical SEES and TCS of some d-metals evidences the prevailing role of the bulk BS effects in the formation of spectra.
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And there occurs a possibility for the experimental study of electron dispersion in the region of energies much higher than Evac and for usage of the SEES and TCS data in a more perfect calculation of BS showing which singularities of the spectra relate to some or other bands. Investigation and interpretation of the experimental SEES and TCS at different angles of PEs incidence can give a straightforward information on the bulk BS features in all Brillouin zone. It can be used (together with VLEED [4,50]) for the analysis of the PES and IPES data. Alongside with singularities responding to the bulk BS, the singularities connected with the electron transitions with the participation of surface states develop in the spectra hsee Fig. 2 for TCS and Ref. [9] for SEES of the clean Ir(111) surface (G LK azimuth) and with (231)O overlayerj. The method being developed enables one to distinguish between the bulk effects in the SEES and TCS and the surface ones which are to be investigated separately.
Acknowledgements This work was supported by the Government Fund for Basic Research of Ukraine.
References [1] J.C. Fuggle, J.E. Inglesfield (Eds.), Unoccupied Electronic States, Springer-Verlag, Berlin, 1992. [2] A. Goldmann, W. Altmann, V. Dose, Solid State Commun. 79 (1991) 511. [3] A.B. Hayden, T. Valla, D.P. Woodruff, J. Phys. Condens. Matter 7 (1995) 9475. ¨ [4] V.N. Strocov, R. Claessen, G. Nicolay, S. Hufner, A. Kimura, A. Harasawa, S. Shin, A. Kakizaki, H.I. Starnberg, P.O. Nilsson, P. Blaha, Phys. Rev. B 63 (2001) 205108. ¨ [5] M. Rosler, in: Particle Induced Electron Emission I, Springer Tracts in Modern Physics, Vol. 122, Springer, Berlin, 1991, p. 1. [6] S.A. Komolov, Total Current Spectroscopy of Surface, Gordon and Breach, Philadelphia, PA, 1992. [7] N.E. Christensen, R.F. Willis, J. Phys. C Solid State Phys. 12 (1979) 167. ¨ ¨ [8] I. Schafer, M. Schluter, M. Skibowski, Phys. Rev. B 35 (1987) 7663. [9] J.U. Mack, E. Bertel, F.P. Netzer, D.R. Lloyd, Z. Phys. B Condens. Matter 63 (1986) 97. [10] B. Lang, Surf. Sci. 66 (1977) 527.
16
O.F. Panchenko / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 11–16
[11] M.P. Seah, Surf. Sci. 17 (1969) 132. [12] V.A. Novolodsky, O.M. Artamonov, S.A. Komolov, Technical. Phys. 44 (1999) 99. [13] A. Otto, B. Reihl, Phys. Rev. B 41 (1990) 9752. [14] P.E. Best, Phys. Rev. B 19 (1979) 2246. [15] V.M. Shatalov, O.F. Panchenko, O.M. Artamonov, A.G. Vinogradov, A.N. Terekhov, Solid State Commun. 68 (1988) 719. [16] J.E. Yater, A. Shih, Appl. Surf. Sci. 143 (1999) 219. ¨ ¨ [17] J. Schafer, R. Schoppe, J. Holzl, R. Feder, Surf. Sci. 107 (1981) 290. [18] V.V. Korablev, Yu.A. Kudinov, O.F. Panchenko, L.K. Panchenko, V.M. Shatalov, Phys. Solid State 36 (1994) 1290. [19] L.N. Tharp, E.J. Scheibner, J. Appl. Phys. 38 (1967) 3320. [20] O.M. Artamonov, A.N. Terekhov, Sov. Phys. Solid State 28 (1986) 479. [21] F. Gol«ek, E. Bauer, Surf. Sci. 369 (1996) 415. [22] B. Lang, S. Tatarenko, Solid State Commun. 31 (1979) 303. [23] D.R. Lloyd, F.P. Netzer, Solid State Commun. 45 (1983) 1047. ¨ ¨ [24] J. Schafer, J. Holzl, Thin Solid Films 13 (1972) 81. ¨ [25] H. Hopster, R. Raue, E. Kisker, G. Guntherodt, M. Campagna, Phys. Rev. Lett. 50 (1983) 70. [26] T. Koshikawa, R. Shimizu, K. Goto, K. Ishikawa, J. Phys. D Appl. Phys. 7 (1974) 462. ¨ [27] E. Kisker, W. Gudat, K. Schroder, Solid State Commun. 44 (1982) 591. [28] G. Appelt, Phys. Status Solidi 27 (1968) 657. [29] L.H. Jenkins, M.F. Chung, Surf. Sci. 26 (1971) 151. [30] K.K. Kleinherbers, A. Goldmann, E. Tamura, R. Feder, Solid State Commun. 49 (1984) 735. [31] L.H. Jenkins, M.F. Chung, Surf. Sci. 28 (1971) 409. [32] R. Feder, J.B. Pendry, Solid State Commun. 26 (1978) 519. [33] O.F. Panchenko, L.K. Panchenko, Solid State Commun. 89 (1994) 849. [34] O.F. Panchenko, L.K. Panchenko, Solid State Commun. 101 (1997) 483. [35] S.A. Komolov, L.T. Chadderton, Surf. Sci. 90 (1979) 359. [36] S. Komolov, E. Lazneva, P.J. Møller, Surf. Sci. 323 (1995) 102.
[37] R.C. Jaklevic, L.C. Davis, Phys. Rev. B 26 (1982) 5391. [38] A. Dittmar-Wituski, P.J. Møller, Surf. Sci. 287–288 (1993) 577. ~ Lindgren, L. Wallden, ´ J. Rundgren, P. Westrin, Phys. Rev. [39] A. B 29 (1984) 576. [40] E. Tamura, R. Feder, J. Krewer, R.E. Kirby, E. Kisker, E.L. Garwin, F.K. King, Solid State Commun. 55 (1985) 543. [41] R. Drube, J. Noffke, R. Schneider, J. Rogozik, V. Dose, Phys. Rev. B 45 (1992) 4390. [42] J.-V. Peetz, W. Schattke, H. Carstensen, S. Ritt, R. Manzke, M. Skibowski, Phys. Rev. B 46 (1992) 10127. ˇ M.A. Van Hove, M.S. Altman, Surf. Sci. 352–354 [43] I. Bartos, (1996) 660. [44] S.A. Komolov, O.F. Panchenko, L.K. Panchenko, Phys. Solid State 38 (1996) 1733. [45] O.F. Panchenko, L.K. Panchenko, Phys. Lett. A 192 (1994) 289. [46] J. Noffke, L. Fritsche, J. Phys. F Metal Phys. 12 (1982) 921. [47] V.V. Nemoshkalenko, V.N. Antonov, Computational Physics Methods in Solid State Theory, The Band Theory of Metals, Naukova Dumka, Kiev, 1985, in Russian. [48] P.N. Ray, J. Chowdhuri, S. Chatterjee, J. Phys. F Metal Phys. 13 (1983) 2569. [49] K.C. Prince, Photoelectron Spectroscopy of Solids and Surfaces, in: Synchrotron Radiation Techniques and Applications, World Science Publishers, London, 1999. ¨ [50] S. Hufner, R. Claessen, F. Reinert, Th. Straub, V.N. Strocov, P. Steiner, J. Electron Spectrosc. Relat. Phenom. 100 (1999) 191. ` [51] D. Pines, P. Nozieres, The Theory of Quantum Liquids, Normal Fermi Liquids, Vol. 1, Benjamin, New York–Amsterdam, 1966. [52] O.F. Panchenko, L.K. Panchenko, J. Electron Spectrosc. Relat. Phenom. 83 (1997) 21. ¨ [53] J.A. Schafer, Surf. Sci. 148 (1984) 581. [54] W.S. Vogan, S.G. Walton, R.L. Champion, Surf. Sci. 459 (2000) 14. [55] H.J. Hopman, H. Zeijlemaker, J. Verhoeven, Appl. Surf. Sci. 171 (2001) 197.
Unoccupied electronic band structure effects in low-energy SEES and TCS of some d-metals O.F. Panchenko* A. A. Galkin Donetsk Institute of Physics and Technology, Ukrainian National Academy of Sciences, 72 Rozy Luxemburg Street, 83114 Donetsk, Ukraine
Abstract The fine structure of the experimental secondary electron emission spectra (SEES) along the normal to a Ir(111) surface and the target (total) current spectra (TCS) along the normal to a Cu(111) surface are interpreted theoretically. It is shown that the fine structure of SEES and TCS is mainly due to the electronic structure of unoccupied high-level electronic states (above the vacuum level Evac ) to which the electrons come or from which they emit. The predominant role of the effects of bulk energy-band structure in the formation of spectra is shown. Comparison to existing experimental data is given. 2002 Elsevier Science B.V. All rights reserved. Keywords: Low-energy electrons; Secondary electron emission spectra; Target (total) current spectra; Fine structure; Band structure; d-Metals
1. Introduction The electronic band structure (BS) is a fundamental characteristic that predetermines a majority of solid state features [for example, transfer phenomena, optical and photoemission (PES) features]. It is also one of the major factors in determining the functioning of solid state electronic devices. The traditional research methods as regards the unoccupied high-level electronic states are: X-ray absorption spectroscopy (XAS) [1], bremsstrahlung isochromat spectroscopy (BIS) [2], inverse PES (IPES) [3], very low-energy electron diffraction (VLEED) [4], and low-energy secondary electron spectroscopy. The latter is characterized by the high surface sensitivity and the absence of destructive impact on an investigated sample. The secondary electron *Tel.: 1380-622-553-585. E-mail address: [email protected] (O.F. Panchenko).
spectroscopy, based on the study of phenomena accompanying the process of interaction between the flow of slow-moving primary electrons (PEs) Ip (with energy Ep #1 keV) and crystal surface, consists of two methods [5,6]: differential and integral ones. The former gives the distribution curve by the energy of secondary electrons (SEs) outside the crystal or secondary electron emission spectra (SEES). The latter gives the curve of the integrated (or total) current of SEs in the sample or target (total) current spectra (TCS). The main features of the fine structure (FS) of SEES and TCS, showing the whole complex of phenomena taking place in the near-surface layer, are mainly connected with the bulk BS of the crystal [7,8]. SE-emission of metals has been experimentally investigated by many authors; in most cases the objects of investigation were polycrystals. The FS at the background of SEES cascade maximum (CM) was, for example, observed in the energy distribution
0368-2048 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 02 )00167-6
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of SEs of the Ir [9], Pt [10], Ag [11–13], Si [14–16], W [7,17–21], Pd [22,23], Ni [24,25], Fe [26,27], Cu [28–30], and Al [31] single crystals. The theoretical analysis of SEES turned out to be rather difficult because it was necessary to take into consideration all the physical processes taking place at the interaction of PEs flow with the crystal. The experimentally observed FS of SEES could not be explained by the theories within the model of free electrons without taking account of the BS. Calculations of the SEES done in Ref. [7] have shown how the FS relates to the bulk density of states r (E); there only the spectral line position (but not shape and intensity) has been analysed with neglect of the energy level broadening. The FS of SEES has been interpreted in Refs. [13,17,30,32] basing on the theory of LEED. The results of Ref. [17] differ from those of Refs. [7,32] though they satisfactorily describe the FS of the experimental curves. In Ref. [9] the experimental angle-resolved SEES are interpreted as emission from excited bulk bands (some additional features are interpreted as surface resonances) without any theoretical calculations. In so doing, the BS E(k) of the conduction band is calculated by construction of energy Ei of the spectrum peaks as the function of angle emission k. In Refs. [15,18,33,34] it is shown that the FS of SEES is determined by the energy dispersion of unoccupied high-level electronic states and represent the boundaries of bands in the dispersion of electrons moving in direction of detection. A comparatively small number of papers (see, e.g., Refs. [6,8,12,35–42]) has been devoted to the investigation of the TCS—the derivative with respect to Ep from total current in circuit of a sample I5Ip 2Is , where Is is the current of electrons, both elastically (including the intensity of specularly reflected elastic beam I00 measuring in the LEED experiments) and inelastically reflected, emitted from the sample. According to Refs. [6,12,35,36], in the energy range to 100 eV the electron–electron (e–e) scattering with the excitation of interband transitions prevails, and the main structures in the TCS represent the peculiarities of r (E). A relation between the FS of TCS and the bulk BS is also confirmed by calculations done in Refs. [37,39,40,43] by using the LEED theory. The aim of this paper is to elucidate the reg-
ularities of SEES and TCS FS formation, their relation with the bulk BS and to develop a technique for the processing of experimental results to obtain the maximum of information on the electron dispersion above Evac . As before (see, e.g., Refs. [15,18,44,45]) during the calculation of the Ir(111) SEES and the Cu(111) TCS the electron scattering with a preset momentum at the crystal was considered within the approximation, when the probability of scattering was proportional to a number of finite states at a given level of energy E with a preset direction of quasi-momentum V. The energy dependence of the band energy level broadening "G (E) 5 " /t (E), the e–e and electron–plasmon contribution to the nonequilibrium SEs-distribution function f(E), the isotropic component of current from the electrons scattered on the surface were taken into consideration. The paper is based on real BS Enk and r (E) [46–48]. Enk enters the calculations of spectra through N(E,V ) (see, e.g., Fig. 1a) is the number of the energy bands along direction V, for which the equality E5Enk is satisfied. As to the taking into consideration the surface effects which contribute to the formation of N(E,V ), the following can be said. The specific features of the electronic spectrum of metal surface are connected with the fact that the electronic spectrum, typical of the bulk, is not practically disturbed in the near-surface region, and the local surface states appear only on its background. This is confirmed by the data of numerous PES investigations (see, for example, Refs. [49,50]). The geometric structure of surface lattices of atomicpure metal surfaces does not, as a rule, differ from the structure of the bulk.
2. Results of the SEES calculation Fig. 1b shows the results of SEES calculation along the normal to a Ir(111) surface with the attraction of the bulk BS obtained by different authors. The background component of current—a structureless CM (peak A in Fig. 1) was taken into account by the addition of constant C to N(E,V ) when the electronic structure of the near-surface region is described by a model of nearly free electron gas. As is shown in Ref. [15], the varying of C in a
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Fig. 1. (a) A number of Ir electron dispersion branches [46] (L6 1 , L6 2 , G6 2 , G7 2 , G8 2 its points of symmetry) that intersect the level E along the direction V ; (b) the SEES along the normal to a (111) surface: (1) experiment (from Ref. [9] for the G LW azimuth) for Ep 540 eV; (2) theory based on BS calculations [46] at Epl 50.96 eV; (3)–(5) theory based on BS calculations [46–48], respectively, at Epl 50.27 eV. Curves 1–5 are plotted on the ordinate arbitrarily. The energy E refers to Evac . Vertical dotted lines with the lettering A–D show the main singularities of the experimental SEES.
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wide limit from 0 to 100 does not practically change the type of second derivative J0(E,V ) which is explained by a small dependence of J0(E,V ) on the background component for all E, except for the neighborhood of CM. For J(E,V ) calculation the following values of parameters have been used: C5 4 (gives CM shape and width close to the experiment); Evac 5EF 1ew, where EF 510.8 eV and ew 5 5.8 eV. A range of parameters used in our calculations does not significantly influence the final results. The work function ew determines only the initial energy reading both for SEES along the normal to a Ir(111) surface and for TCS (see below) along the normal to a Cu(111) surface. We refer to ew as a parameter because there exist certain variations in how to determine its value. For example, according to the reference data for Ir(111): ew 55.7460.06 eV and ew 55.860.03 eV (method of thermoelectron emission); ew 55.7960.03 eV (method of surface ionization of atoms). It is obvious that our chosen value ew conforms well, within the tolerance limits of the measurements, to these data. Similarly, we used ew 54.2 eV for Cu(111) (according to Ref. [6]). The Fermi level EF was selected from the calculations of the BS used by us [46–48]. Thus, for Ir: EF 510.8 eV (according to Ref. [46]), EF 510.76 eV [48], and EF |11 eV [47]; for Cu: EF 59.2 eV [47]. The variation of the EF value within 0.2 eV does not significantly influence the final result which is of qualitative rather than quantitative nature. It also correct because, besides the error of our calculations, there exists the error (#0.5 eV) for experimental curves which we have provided so that you could use them as a base for comparison with our calculations. The lifetime of the excited state t (E) was determined from Ref. [51]: " /t (E)5Epl (E /EF 21)2 , where Epl is the screening parameter. The occupation states function f(E), responding to the multiple e–e scattering, has been obtained in Ref. [52] at E2EF , ,Ep by solving a system of transport equations within the approximation of e–e scattering statistical model. This system describes the cascade process of the inelastic scattering of the PEs flow. The decay of plasmons, generated by the PEs as well as by the excited electrons in a solid, contributes to f(E) which, when neglecting the plasmon dispersion, has been obtained from the energy conservation law [52].
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Curve 3 the best agrees with the FS (peaks B, C and D) of experimental spectrum [9] (curve 1), when the parameter of broadening Epl , depending on concentration of s- and d-electrons in the electronic shell of an atom, was calculated starting not from the general theory of metals (as for curve 2) but was a fitted one. This is because t (E), responsible for peak broadening and used in calculations, has been obtained in Ref. [51] near the Fermi surface and not in the region of high-lying excited states. Position and intensity of the FS maxima C and D on curve 4 are essentially different from analogous peculiarities of the experimental spectrum which is because of the approximate calculations of the BS [47] within the RAPW method for E $15 eV above EF . With the BS calculation [48] within the RKKR method, to identify the FS of the experimental spectrum (see curve 5) was not a success. As is seen from Fig. 1, the jumps of the function N(E,V ) correspond to extreme values of J(E,V ). These jumps or thresholds are formed at boundaries of bands of the resolved energy values for each of the energy bands. Presence of large background component in the Ir(111) SEES in the neighborhood of CM (Fig. 1, curve 1) disables one to distinguish between the bulk and surface effects in the spectrum ha similar situation was observed by us in Ref. [34] during the interpretation of the Ge(111) SEESj. As is shown in Refs. [15,25], the double differentiation of the spectrum could eliminate these difficulties. Apart from this, separation of the bulk and surface properties is also possible when investigating the SEES under the absorption of dissimilar particles [9,10,20,22,53–55]. And the change of FS features serves a measure of the presence of defects in the near-surface layer of the sample, which can be successfully used to control surface states during the processing.
3. Results of the TCS calculation The results of the TCS S(E,V ) calculation (Epl 54 eV) are shown in Fig. 2 (curves 3, 4) for Cu(111). In Fig. 2 (curves 1, 2, 5 and dashed curve) the experimental TCS [4,6,37,39] are shown for comparison. The spectra have the FS which is essentially dependent on single-crystal orientation. The intensity
Fig. 2. TCS along the normal to a Cu(111) surface: (1), (2) the experimental results dI(E,V ) / dE from Refs. [6,39], respectively hdashed curve represents the TCS data dI(E,V ) / dE from Ref. [4] on the unrelaxed (111) surfacej; (3) theory dI(E,V ) / dE; (4) theory d 2 I(E,V ) / dE 2 ; (5) experiment d 2 I(E,V ) / dE 2 from Ref. [37]. Curves 1–5 are plotted on the ordinate arbitrarily. The energy E refers to Evac . The positions of TCS typical maxima are denoted by a, b, c, . . . , f 9 in increasing energy.
of FS|1% of the value of PEs-distribution maximum (in figures it is absent), which occurs at the energy when the electrons start hitting the sample. The main peculiarities of the Cu(111) TCS (the maxima c–g) are in agreement with the representations on the bulk BS in the near-surface region. On the background of spectrum structure corresponding to the bulk (discussed in Ref. [44]), the maxima a, b (curve 1) and b9 (curve 5) are observed, the formation of which is connected with the excitation of electrons from the occupied states located near EF . These states are the
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surface ones, they develop only in the experiments [6,37] and are not registered in the experiments [4,39], and are absent on the theoretical curves, constructed without considering both elastic scattering and the surface structure and states. Differences in the position of singularities on theoretical and experimental curves are connected (as was stated above) on one hand, with the approximate character of BS calculation for high-lying levels [47] (according to Ref. [4], the unoccupied high-level electronic states, contrary to the universally accepted point of view, can be characterised by considerable deviations from the free electron dispersion, and influenced by multi-electronic effects). On the other hand, there exist the experimental errors connected with the formation of collimated electron beam in the region of low energies, realization of the total collection of SEs, etc. Thus, the energy position and the intensity of maxima in the TCS of Cu(111) highly depend on the angle of primary beam incidence [4,35]. Singularity d (curve 1) abruptly decreases when the electron beam deviates from the normal to the surface. In the experiment this fact was used as a criterion of conditions for the normal incidence of primary beam. Singularities a, b and b9 can be explained by both the high surface sensitivity of the TCS determined not only by a small depth of the analysed region, but by a high dependence on the physical and chemical surface processes [36,38], and the deviation of the electron beam from the normal, with some error in the orientation of faces. Note that the absorption of residual gases (|10 22 Pa) on a Cu(111) surface or the ionic bombardment thereof also results in maxima a and b vanishing; subsequent desorption of residual gases is accompanied by the restoration of their intensity [6]. The absorbents or dissimilar atoms and defects present on the surface result in the large-angle elastic scattering, thus opening new channels for the electron penetration to the crystal.
4. Conclusion The obtained correspondence between the main features of experimental and theoretical SEES and TCS of some d-metals evidences the prevailing role of the bulk BS effects in the formation of spectra.
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And there occurs a possibility for the experimental study of electron dispersion in the region of energies much higher than Evac and for usage of the SEES and TCS data in a more perfect calculation of BS showing which singularities of the spectra relate to some or other bands. Investigation and interpretation of the experimental SEES and TCS at different angles of PEs incidence can give a straightforward information on the bulk BS features in all Brillouin zone. It can be used (together with VLEED [4,50]) for the analysis of the PES and IPES data. Alongside with singularities responding to the bulk BS, the singularities connected with the electron transitions with the participation of surface states develop in the spectra hsee Fig. 2 for TCS and Ref. [9] for SEES of the clean Ir(111) surface (G LK azimuth) and with (231)O overlayerj. The method being developed enables one to distinguish between the bulk effects in the SEES and TCS and the surface ones which are to be investigated separately.
Acknowledgements This work was supported by the Government Fund for Basic Research of Ukraine.
References [1] J.C. Fuggle, J.E. Inglesfield (Eds.), Unoccupied Electronic States, Springer-Verlag, Berlin, 1992. [2] A. Goldmann, W. Altmann, V. Dose, Solid State Commun. 79 (1991) 511. [3] A.B. Hayden, T. Valla, D.P. Woodruff, J. Phys. Condens. Matter 7 (1995) 9475. ¨ [4] V.N. Strocov, R. Claessen, G. Nicolay, S. Hufner, A. Kimura, A. Harasawa, S. Shin, A. Kakizaki, H.I. Starnberg, P.O. Nilsson, P. Blaha, Phys. Rev. B 63 (2001) 205108. ¨ [5] M. Rosler, in: Particle Induced Electron Emission I, Springer Tracts in Modern Physics, Vol. 122, Springer, Berlin, 1991, p. 1. [6] S.A. Komolov, Total Current Spectroscopy of Surface, Gordon and Breach, Philadelphia, PA, 1992. [7] N.E. Christensen, R.F. Willis, J. Phys. C Solid State Phys. 12 (1979) 167. ¨ ¨ [8] I. Schafer, M. Schluter, M. Skibowski, Phys. Rev. B 35 (1987) 7663. [9] J.U. Mack, E. Bertel, F.P. Netzer, D.R. Lloyd, Z. Phys. B Condens. Matter 63 (1986) 97. [10] B. Lang, Surf. Sci. 66 (1977) 527.
16
O.F. Panchenko / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 11–16
[11] M.P. Seah, Surf. Sci. 17 (1969) 132. [12] V.A. Novolodsky, O.M. Artamonov, S.A. Komolov, Technical. Phys. 44 (1999) 99. [13] A. Otto, B. Reihl, Phys. Rev. B 41 (1990) 9752. [14] P.E. Best, Phys. Rev. B 19 (1979) 2246. [15] V.M. Shatalov, O.F. Panchenko, O.M. Artamonov, A.G. Vinogradov, A.N. Terekhov, Solid State Commun. 68 (1988) 719. [16] J.E. Yater, A. Shih, Appl. Surf. Sci. 143 (1999) 219. ¨ ¨ [17] J. Schafer, R. Schoppe, J. Holzl, R. Feder, Surf. Sci. 107 (1981) 290. [18] V.V. Korablev, Yu.A. Kudinov, O.F. Panchenko, L.K. Panchenko, V.M. Shatalov, Phys. Solid State 36 (1994) 1290. [19] L.N. Tharp, E.J. Scheibner, J. Appl. Phys. 38 (1967) 3320. [20] O.M. Artamonov, A.N. Terekhov, Sov. Phys. Solid State 28 (1986) 479. [21] F. Gol«ek, E. Bauer, Surf. Sci. 369 (1996) 415. [22] B. Lang, S. Tatarenko, Solid State Commun. 31 (1979) 303. [23] D.R. Lloyd, F.P. Netzer, Solid State Commun. 45 (1983) 1047. ¨ ¨ [24] J. Schafer, J. Holzl, Thin Solid Films 13 (1972) 81. ¨ [25] H. Hopster, R. Raue, E. Kisker, G. Guntherodt, M. Campagna, Phys. Rev. Lett. 50 (1983) 70. [26] T. Koshikawa, R. Shimizu, K. Goto, K. Ishikawa, J. Phys. D Appl. Phys. 7 (1974) 462. ¨ [27] E. Kisker, W. Gudat, K. Schroder, Solid State Commun. 44 (1982) 591. [28] G. Appelt, Phys. Status Solidi 27 (1968) 657. [29] L.H. Jenkins, M.F. Chung, Surf. Sci. 26 (1971) 151. [30] K.K. Kleinherbers, A. Goldmann, E. Tamura, R. Feder, Solid State Commun. 49 (1984) 735. [31] L.H. Jenkins, M.F. Chung, Surf. Sci. 28 (1971) 409. [32] R. Feder, J.B. Pendry, Solid State Commun. 26 (1978) 519. [33] O.F. Panchenko, L.K. Panchenko, Solid State Commun. 89 (1994) 849. [34] O.F. Panchenko, L.K. Panchenko, Solid State Commun. 101 (1997) 483. [35] S.A. Komolov, L.T. Chadderton, Surf. Sci. 90 (1979) 359. [36] S. Komolov, E. Lazneva, P.J. Møller, Surf. Sci. 323 (1995) 102.
[37] R.C. Jaklevic, L.C. Davis, Phys. Rev. B 26 (1982) 5391. [38] A. Dittmar-Wituski, P.J. Møller, Surf. Sci. 287–288 (1993) 577. ~ Lindgren, L. Wallden, ´ J. Rundgren, P. Westrin, Phys. Rev. [39] A. B 29 (1984) 576. [40] E. Tamura, R. Feder, J. Krewer, R.E. Kirby, E. Kisker, E.L. Garwin, F.K. King, Solid State Commun. 55 (1985) 543. [41] R. Drube, J. Noffke, R. Schneider, J. Rogozik, V. Dose, Phys. Rev. B 45 (1992) 4390. [42] J.-V. Peetz, W. Schattke, H. Carstensen, S. Ritt, R. Manzke, M. Skibowski, Phys. Rev. B 46 (1992) 10127. ˇ M.A. Van Hove, M.S. Altman, Surf. Sci. 352–354 [43] I. Bartos, (1996) 660. [44] S.A. Komolov, O.F. Panchenko, L.K. Panchenko, Phys. Solid State 38 (1996) 1733. [45] O.F. Panchenko, L.K. Panchenko, Phys. Lett. A 192 (1994) 289. [46] J. Noffke, L. Fritsche, J. Phys. F Metal Phys. 12 (1982) 921. [47] V.V. Nemoshkalenko, V.N. Antonov, Computational Physics Methods in Solid State Theory, The Band Theory of Metals, Naukova Dumka, Kiev, 1985, in Russian. [48] P.N. Ray, J. Chowdhuri, S. Chatterjee, J. Phys. F Metal Phys. 13 (1983) 2569. [49] K.C. Prince, Photoelectron Spectroscopy of Solids and Surfaces, in: Synchrotron Radiation Techniques and Applications, World Science Publishers, London, 1999. ¨ [50] S. Hufner, R. Claessen, F. Reinert, Th. Straub, V.N. Strocov, P. Steiner, J. Electron Spectrosc. Relat. Phenom. 100 (1999) 191. ` [51] D. Pines, P. Nozieres, The Theory of Quantum Liquids, Normal Fermi Liquids, Vol. 1, Benjamin, New York–Amsterdam, 1966. [52] O.F. Panchenko, L.K. Panchenko, J. Electron Spectrosc. Relat. Phenom. 83 (1997) 21. ¨ [53] J.A. Schafer, Surf. Sci. 148 (1984) 581. [54] W.S. Vogan, S.G. Walton, R.L. Champion, Surf. Sci. 459 (2000) 14. [55] H.J. Hopman, H. Zeijlemaker, J. Verhoeven, Appl. Surf. Sci. 171 (2001) 197.