The energy dependence of the electron inelastic scattering mean-free-path in gold

Solid State Communications, Vol. 22, pp. 711 —713, 1977.

Pergamon Press.

Printed in Great Britain

THE ENERGY DEPENDENCE OF THE ELECTRON INELASTIC SCA11’ERING MEAN-FREE-PATh IN GOLD D. Norman and D.P. Woodruff Physics Department, University of Warwick, Coventry CV4 7AL, U.K. (Received 19 January 1977 by C. W. McCombie) The relative electron inelastic scattering mean-free-path in gold in the energy range 60—140 eV has been determined by the overlayer technique using synchrotron radiation photoemission spectroscopy from the 4f core levels of a tantalum foil substrate. The mean-free-path falls rapidly from 60 to 80eV but is essentially constant from 100 to 140 eV. THE MEAN-FREE-PATH for inelastic scattering of electron having kinetic energies 10—2000eV is an extremely important parameter in surface physics as it defines the degree of surface specificity of some of the most widely used and valuable experimental techniques. In particular the chemical composition techniques of Auger Electron Spectroscopy (AES) and X.ray Photoelectron Spectroscopy (XPS) as well as Ultra-violet Photoelectron Spectroscopy (UPS) and the structural technique of Low Energy Diffraction (LEED) all involve the analysis of electrons which have passed through the surface region of the material being analysed without loss ofenergy (neglecting phonon effects). The depth of surface analysis is therefore of the order of the meanfree-path for inelastic scattering of these electrons in the material under study. Most of the experimental measurements of this parameter have been by a direct technique [1]. A substrate material having Auger electron or photoelectron emissions (with a standard associated laboratory X-ray source) at suitable energies is chosen and the attenuation of the emitted AES or XPS signal from this substrate is studied as known amounts of some foreign species are added to the surface. This permits a direct determination ofthe mean-free-path of electronsofenergies determined by the AES or XPS spectra of the substrate, within the material of the adsorbate or overlayer. l’his approach has allowed a number of measurements to be made, especially in some common metals, at energies in the range of interest [1—3].The main limitation of the method is that it is difficult to determine the electron energy dependence of the mean-free-path with any precision. The chosen substrate is unlikely to provide more than two or three fixed energy emissions widely distributed over the 10—2000eV range. Of course, with patience, a range of different substrates can be used to provide additional energies. Apart from the rather laborious nature of this approach, however, a change of substrate to find new emission energies means that the relative values of the mean-free-path at energies 711

associated with different substrates is limited by the absolute accuracy of individual measurements. As the principal error in these measurements results from the calibration of the overlayerthickness (typically 1—20 A) this approach is also rather unsuitable. Evidently the ideal method of tackling this problem is to use a technique which provides an electron emission from the substrate whose energy is variable in some way. Synchrotron radiation photo-electron spectroscopy provides such a techniqe. By using a source of photons of variable energy (monochromated synchrotron radiation)the kinetic energy of photoemitted electrons from some substrate core level can similarly be varied. Here we report the first measurements made by this technique. Our experiments were performed in a standard V.G. Scientific ESCA III photoelectron spectrometer deriving its light source from NINA, the 5 GeV electron synchrotron at the Daresbury Laboratory of the Science Research Council. The grazing incidence monochromator provided a good photon flux for our purposes over the energy range 70—170 eV. The choice of a suitable substrate is dictated partly by the constraints of experimental convenience (easy to prepare clean surfaces which are stable in Ivacuo) and partly by the need for a core level, sufficiently deep to be well localised but sufficiently shallow to be readily accessible over the whole photon range available. This defmes the necessary core level energy to be 20—50 eV. Evidently a large photoionisation cross-section is required and this greatly favours high i-value states (d or f states). Finally, a state with the 1 quantum value equal to the n quantum number is preferred; states with n >1 show strong variations of photoionisation cross-section with photon energy and in particular the cross-section may be very low in a range of energies associated with a Cooper minimum [41.In order to avoid the complicating effects of anisotropic emission [5, 6], we also need a polycrystalline substrate. For these initial experiments we have used a Ta foil substrate; this material has a satisfactory 4f (doublet) level at a binding energy of

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ELECTRON INELASTIC SCA11~ERINGMEAN-FREE-PATH IN GOLD

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substrate. As a check on the consistency of the measurements and to check for significant effects due to island

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growth, relative mean-free-paths were calculated using the ratio of signals from the two coverages as well as the ratio of covered to clean. Mean-free-paths were normal. I

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Vol. 22, No.11

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Fig. 1. Relative and absolute mean-free-paths in gold. Data points X are relative intensities from this work (see left hand axis). Data points 0 are due to Kanter [8] while the remaining points are due to Lindau et al. [7]. These data are absolute values (see right hand axis). about 26 eV. The only disadvantage of this material is that the 4f level has a significant centrifugal barrier leading to delayed onset [4]; as a result, at the lowest photon energies available (70—80 eV) the photoionisation cross-section is still quite small and rather weak 4f level peaks are seen in the photoemission spectra. The measurements we report here were taken on gold overlayers. The Ta foil was cleaned by argon ion bombardment and heating and after characterising the intensity of the 4f emissions from the clean substrate, gold was evaporated from a tungsten filament surrounded by a liquid nitrogen cooled sleeve to minimise the problems of outgassing. No measurement of the thickness of the evaporated film was made; the constraints of equipment access in the synchrotron radiation facility make careful and precise measurements impossible so instead we concentrate on the relative values of mean-free-paths which may be deduced without a knowledge of the film thickness. Two separate sets of measurements were made, each for two different coverages on the same

ised in each case to a relative value of 1.0 at a photon energy of 120 eV. Agreement of all results was satisfactory within the calculated statistical errors (including those errors associated with the measurements at the point of normalisation); no systematic behaviour indicative of strong islanding was seen. Figure 1 shows our results plotted as relative meanfree-paths (left-hand-scale) against energy above the Fermi level. The binding energy of the 4f levels was taken as 23 eV below the Fermi level (the exact value is imprecise as we integrated areas over a 6 eV range to include the whole doublet peak). No error is shown on the Errors value atfor97eV this was the nonnalisation point. otheraspoints indicate the scatter of individual measurements but are also typically of the order of the statistical errors in individual measurements. The exceptionis the point at 57 eV (80 eV photon energy). Errors in individual measurements at this energy were large the combined effects of poorer statistics (due todue theto relatively weak photoionisation crosssection and the need to subtract high backgrounds), but more particularly because the increasing mean-free-path results in lower attenuation and so a ratio ofpeak areas close to unity. Evidently as the relative mean-free-path is proportional to the reciprocal of the logarithm of this ratio, a small error in the ratio has a profound effect on the error of the derived mean-free-path. The result at 57 eV in Fig. 1 is therefore from two results only. Other results agreed with these but showed much larger errors (particularly on the high value side). While the statistics of the low energy values is poor, a clear upward trend of mean-free-path is seen. There is some evidence for a weak minimum at 90eV but values above this energy are essentially constant. For comparison we also show on Fig. 1 the results of Lindau et al. [7] based on an indirect analysis of photoemission data, and a few of Kanter’s data [8] (these data extend to lower energies but have been omitted to preserve an expanded scale in the region of our own data). Both of these earlier sets of data are absolute values and to draw them on Fig. 1 we have matched our results to those of Lindau in the region of overlap. While we should be cautious of inferring absolute values of the mean-freepath for our data in this way, there is clear agreement in the trend in the region of overlap. In particular, the results of Lindau et al. show a steady fall in mean-freepath from 25 to 75 eV with only the slightest hint of leveffing out at the high energy end. Our own results ‘—

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ELECTRON INELASTIC SCAUERING MEAN-FREE-PATH IN GOLD

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match the fall at the high energy end of this range and free-path for gold should occur at somewhat higher show it becomes essentially constant beyond. energy (— 70—90 eV). This appears to be in general The only theoretical predictions of the general beagreement with our findings and with the overall shape haviour of the mean-free-path in this general energy indicated by all the results of Fig. 1. range are based on calculations of plasmon creation in RPA but applied to an electron density appropriate to Acknowledgements The authors would like to acknowaluminium. These show a rapid decrease as the energy ledge the financial assistance of the Science Research increases above the plasmon threshold (15 eV) to about Council both in the form of equipment grants and the 2to 3 times this energy where a weakminimumis found; availability of the Synchrotron Radiation Facility (SRF), at higher energies the mean-free-path increases slowly and in the form of a research assistantship for one of [1, 9]. The contribution of single particle exictations us (D.N.). They are also pleased to acknowledge the collaboration of the other members of the joint Photoin the low energy range has also been estimated but does emission Electron Spectroscopy group at Daresbury not strongly affect the shape in the vicinity of the mini- (from the University of Leicester and the New University mum [9]. Evidently the plasmon energy in a noble metal of Ulster) in the general running of our joint instrumensuch as gold is less well-defined than in free-electron-like tation and in some preliminary experiments. Our thanks are also due to all users of the S.R.F. North Line at aluminium. However, both a theoretical and experimen- Daresbury Laboratory for their constant cooperation tal determination of the plasmon energy in gold (30 and and to Professor A.J. Forty for his active interest and 24eV [10]) suggests that this minimum in the meanencouragement in this work. —

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