The normalization of ejected-electron spectra using Auger peaks

JOURNAL OF ELECTRON SPECTROSCOPY and RelatedPhenomena

ELSEVIER

Journal of Electron Spectroscopy and Related Phenomena 77 (1996) 277-281

The normalization of ejected-electron spectra using Auger peaks D.B. Thompson,

N.L.S. Martin*

Department of Physics and Astronomy, University of Kentucky, Lexington, KY40506-0055, USA

Received 14 June 1995;acceptedin final form 14 October 1995

Abstract A technique is described that uses Auger peaks to correct pairs of ejected-electron spectra for three types of instrumental effects in a crossed-beam apparatus with an atomic cadmium target. By comparing Auger peaks that occur in autoionizing spectra taken 180°apart, it is possible to energy-align the spectra to 1 meV, to normalize their relative intensity to 2%, and to correct for different energy resolutions to within 1%.

Keywords: Auger peak; Cadmium; Ejected-electron spectrum; Normalization. PCAS numbers: 07.80. + x, 34.80.DP

1. Introduction We are currently using the coplanar (e, 2e) technique to investigate the overall electron-impact ionization process in cadmium Cd(5s 2 is0) + e0 ~ Cd+(5s2S1/2) + eej + esc in the region of the 4d95s25p autoionizing resonances and for incident electron energy 150 eV. Full details are given in Refs. [1] and [2]; only details pertinent to the subject of this paper will be given here. The experimental method involves the measurement of pairs of (e, 2e) energy spectra, i.e., coincidences observed between scattered and ejected electrons as a function of energy. Each spectrum in the pair is taken at the same scattering angle 0so but at ejected-electron angles 180 ° apart, I(Osc; E, 0ej ) and I(Ose; E, 0ej + 180°); small (approx. 10%) differences in the spectra are due to the sum * Corresponding author.

of interference terms formed from cross-products of multipole amplitudes of different parity. The data analysis isolates the interference cross-terms by forming the difference spectrum [I(0se; E, 0ej)I(0sc; E, 0ej + 180°)]. Since this analysis involves the subtraction of two nearly identical spectra, it is vital to normalize the spectra correctly to one another. The technique we use to do this, and the type of corrections necessary, are the subject of this short paper.

2. Experimental The coplanar (e,2e) spectrometer consists of four main components: an electron gun, a metalvapor atomic beam oven, a scattered-electron spectrometer, and an ejected-electron spectrometer [3]. The electron gun is recessed in a side arm of the vacuum chamber which enables the ejectedelectron spectrometer to be positioned on both sides of the electron beam axis. The metal-vapor

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D.B. Thompson,N.L.S. Martin~Journalof Electron Spectroscopy and RelatedPhenomena 77 (1996) 277-281

oven is an ohmically heated, hollow upright cylinder capped by a collimation nozzle. The interaction region is formed by the intersection of the horizontal electron beam with the vertical atomic beam, which occurs approximately 3 mm above the oven nozzle. The scattered- and ejected-electron spectrometers, which are mounted on concentric turntables, are of similar electron-optical construction. In either case electrons from the interaction region are transported by a three-element lens to the entrance aperture of a hemispherical-sector electrostatic energy analyzer. Electron detection is by means of triple microchannel plate (MCP) assemblies; the ejected-electron detector incorporates a resistive-anode (RA) type position-sensitive detector (PSD). During an experimental run, the scattered-electron detector is kept fixed at the chosen value of 0se and both (e, 2e) spectra andnon-coincident ejectedelectron spectra are collected at the two ejectedelectron angles. To minimize the effect of any drift in the experimental parameters (electron beam, cadmium beam, detector efficiency, etc.), energies and angles are scanned sequentially in the following manner. With the ejected-electron detector set at 0ej, the energy is scanned over the desired range (5 s at each of 576 steps of 0.004 eV in the present experiments; since the PSD channel interval is also 0.004 eV, this compensates for a non-linear response over the MCP area). A stepping motor then rotates the detector to 0ej + 180° where the energy scan is repeated. The detector is then rotated back to 0ej for the start of the next sequence. A typical data set is the result of a continuous experimental run lasting about ten days.

3. Normalization of the spectra Although the (e, 2e) spectrometer incorporates electrostatic and magnetic shielding, there exist small residual a.c. and d.c. fields (of order millivolts and milligauss) which vary across the inside of the vacuum chamber. Because the ejected-electron spectrometer is moved during an experimental run, this leads to differences in three aspects of spectrometer performance for the two positions: (i) there may be a shift in the energy scales of the

spectra due to d.c. magnetic field components normal to the plane containing the electron trajectories through the hemispherical analyzer; (ii) the relative intensities of the spectra may be incorrect due to fields affecting, for example, trajectories through the electron lenses that image the interaction region at the hemisphere entrance aperture; (iii) the energy resolution may be degraded by, for example, a.c. magnetic fields normal to this plane, that "smear out" the spectra along the energy axis. Although these effects are small, they need to be taken into account in our analysis in order that we may have confidence that our results are not due to instrument effects. Because only the ejected-electron detector is moved during an experimental run, the normalization of the (e, 2e) and non-coincident ejected-electron spectra is the same, i.e., we may use the non-coincident spectra to find the correct normalization of the (e, 2e) spectra. Fig. 1 shows a pair of ejected-electron spectra in which can be seen the three Cd 4d95s25p autoionizing resonances. These are superimposed on a smoothly varying background consisting largely of secondary electrons released when the electron beam strikes metal surfaces in the apparatus. Also labelled in the spectra are three very narrow Auger peaks [4]; the measured line shapes are entirely due to the Gaussian instrument function of the electrostatic energy analyzer. The spectrum is taken at 0.004 eV intervals and the resolution is about 0.04 eV; therefore roughly 20 data points span the baseline of a single peak. Because they correspond to double ionization, for which the direct process is negligible, there are symmetries inherent in Auger electron angular distributions [5]. For an unpolarized beam of incident electrons and randomly oriented target atoms, when the scattered and ionized inner shell electrons are not observed, the angular distribution of Auger electrons is both axially symmetric about the incident beam axis and symmetric with respect to reflection in the plane perpendicular to the incident beam axis. Thus, any difference in the shape or magnitude of an Auger resonance, between ejected-electron spectra collected at angles 180° apart, must originate from experimental measurement effects. We are therefore able to correct for the three types of differences listed above by an examination of the Auger peaks;

D.B. Thompson, N.L.S. Mart&/Journal of Electron Spectroscopy and Related Phenomena 77 (1996) 277-281

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their existence is thus crucial to our normalization procedure. Fig. 2(a) shows the difference spectra after the normalization procedure has been carried out. Note that the Auger peaks are absent; the spectrum is almost perfectly smooth in these two energy regions. For this data, there is a relative shift of 0.004 eV for the spectra but the relative intensities require no correction (they rarely require more than a 10% correction). The energy resolution requires a small correction, as described below. Figs. 2(b)-(j) correspond to the energy region indicated in Fig. 2(a); the center figure of each horizontal panel is identical. The panels demonstrate the sensitivity of our normalization procedure by illustrating the characteristic "signatures" caused by each of the three aspects of spectrometer performance listed above in (i)-(iii).

3.1. Correction of energy-shifted spectra Misalignment of ejected-electron energy scales distorts the difference spectrum by introducing a component which is the derivative with respect to energy of nearly identical spectra: I ( E + 6 E ) I(E) ~ (dI/dE)6E, Where 6E is the alignment error. The signature of this distortion is an Y shaped curve (actually the derivative of the Gaussian instrument function) in energy regions where resonances should cancel. The energy scale misalignment signature can be seen in the series of difference spectra Figs. 2(b)-(d) where the relative energy scale is shifted in 0.002 eV steps, through the correct value (linear interpolation is used for steps that are non-integral values of the data point interval of 0.004 eV). This step value was chosen to show the signature clearly; the energy scale of

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Fig. 2. (a) The difference spectrum formed by subtracting the normalized data of Fig. l(b) from that of Fig. l(a). The vertical bars represent the statistical uncertainties. The spectral region between the arrows encompasses the 3.33 eV and 3.35 eV Auger peaks' energy range; (b)-(j) present the spectral variations (signatures) appearing in this range, as the indicated normalization parameter is varied, while holding the others at their correct values (see text).

two ejected-electron spectra may be readily aligned to within 0.001 eV. 3.2. Relative intensity correction

The signature of mismatched intensities is a single

bump or dip with a maximum or minimum located midway between the unresolved Auger peaks. In Fig. 2(e)-(g), the relative intensity is varied in 5% steps through the correct value. Again, this step value has been shown to highlight this signature; the relative intensity can be corrected to about 2%.

D,B. Thompson, N.L.S. Martin~Journal of Electron Spectroscopy and Related Phenomena 77 (1996) 277-281 3.3. Energy resolution correction

This is the least straightforward of the corrections. Empirically, we have found that satisfactory corrections to the resolution may be made by degrading the higher resolution spectrum with a simple algorithm that replaces the ejected-electron spectrum i(E) with [i(E - AE/2) + i(E + AE/2)]/ 2. Here A E is found by trial and error; for values corresponding to non-integral multiples of datapoint spacing, linear interpolation is used. Physically, this correction corresponds to a "double image" and approximately simulates the effect of a stray sinusoidal field where more time is spent at the extremities of the field than at zero field. In fact for small corrections the resultant line shape of a double image closely approximates a Gaussian of increased width. In the spectra of Fig. l, the apparent energy resolution (full width at half maximum, found from the single Auger peak at 4.15 eV) is 0.044 eV for the - 5 0 ° spectrum, and 0.040 eV for the - 2 3 0 ° spectrum. The spectral difference in the double Auger region, without any correction for resolution, is shown in Fig. 2(h). The characteristic signature for the (normally unresolved) twin Auger peaks is a ~V-shaped feature where each dip corresponds to a broad minus a narrow line profile with the same integrated intensity. Fig. 2(j) shows a simulation of a narrow minus a broad line profile, for which the signature of the twin Auger peaks is an J / - s h a p e d feature. The difference spectrum corrected for resolution is shown in Fig. 2(i) where A E = 0 . 0 1 2 eV, or three data-point intervals. Thus the value of A E required is larger than the observed degradation. With the excellent statistics of the present data, A E can be determined to within 0.001 eV, i.e., it should thus be possible to detect differences in resolution of less than 1%.

4. Conclusions We have found that pairs of ejected-electron

281

spectra taken 180 ° apart may be normalized to each other with high accuracy using Auger peaks. The normalization procedure involves three separate steps involving the relative energy scales, intensity scales, and energy resolutions. We are currently planning similar (e, 2e) experiments in helium in the autoionizing ejected-electron energy region 30 to 40 eV. Since there are no Auger processes in helium, we intend to run the experiments in a helium/rare gas mixture; possible candidates are K r and Xe which have prominent Auger lines [6,7] in this energy range. Thus the noncoincident ejected-electron spectra will contain Auger features for normalization purposes, but the presence of either of these gases will not affect the (e, 2e) spectra because their ionization potentials are very different from that of helium.

Acknowledgements This work was supported by a grant from the United States Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Fundamental Interactions Branch, under contract DE-FG05-91ER14214.

References [1] N.L.S. Martin, D.B. Thompson, R.P. Bauman and M. Wilson, Phys, Rev. Lett., 72 (1994) 2163. [2] N.L.S. Martin, D.B. Thompson, R.P. Bauman and M. Wilson, Phys. Rev. A, 50 (1994) 3878. [3] N.L.S. Martin and D.B. Thompson, J. Phys. B, 24 (1991) 683. [4] V. Pejcev,K.J. Ross, D. Rassi and T.W. Ottley, J. Phys. B, 10 (1977) 459. [5] W. Melhorn, in B. Crasemann (Ed.), Atomic Inner-Shell Physics, Plenum, New York, 1985, p. 119. [6] L.O. Werme, T. Bergmark and K. Siegbahn, Phys. Scr., 6 (1972) 141. [7] H. Askela, S. Askela and H. Pulkkinen, Phys. Rev. A, 30 (1984) 865.