Experimental determination of the inelastic mean free path for Cu, Ag, W, Au and Ta, in the energy range 500–3000 eV by elastic peak electron spectroscopy and using Ni reference sample

Vacuum/volume

46/number 5/6/pages 591 to 59411995 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0042-207x/95 $9.50+.00

Pergamon 0042-207x194)00137-s

Experimental determination of the inelastic mean free path for Cu, Ag, W, Au and Ta, in the energy range 500-3000 eV by elastic peak electron spectroscopy and using Ni reference sample* G Gergely, M Menyhard, K Pentek and ASulyok, Research Institute of Sciences, H-1325, P.O. Box 76, Budapest, Hungary A Jablonski and B Lesiak, Institute 01-224 Warszawa, Poland

of Physical

Chemistry,

for Technical

Polish Academy

Physics Hungarian

of Sciences,

Kasprzaka

Academy 44/52,

and Cs Daroczi, Research

Institute

for Material

Science of HAS, H- 1525, P.O. Box 49, Budapest,

Hungary

The inelastic mean free path f/MFPJ is the most important electron transport parameter. The value of iMFP can be determined by electron reflection experiments (EPESI supported by the Monte Carlo theory with the multiple elastic scattering events considered. The values of IMFP for the high atomic number elements obtained from such a model and applying Al standard were found to be in reasonable agreement with the theoretical values. Recently, Ni has been proved to be a more adequate reference sample due to the lack of inelastic losses appearing in the vicinity of the elastic peak. In the present work the energy dependence of the IMFP for Cu, Ag, W, Ta and Au using Ni standard was evaluated by EPES in the energy range 500-3000 eV. The Ni standard of high quality was used, where its surface roughness was verified by scanning tunnelling microscopy. Reasonable agreement with Tanuma et al. results was obtained in the energy range 500-2000 eV. Above 2000 eV the obtained results were in agreement with the values by Ashley and Tung.

1. Introduction The inelastic mean fee path (IMPF) is an important material parameter of crucial importance for quantitative surface analysis by Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), electron energy loss spectroscopy (EELS), elastic peak electron spectroscopy (EPES) as well as for non destructive depth profiling. The sampling depth of electrons (Auger, photoelectrons, loss, elastic) is determined by IMFP, which is defined as an average distance which electrons travel between successive inelastic collisions’. The values of IMFP result mainly from theory. During the last 20 years a great number of papers on the calculation of IMFP have been published. The most reliable results for 27 elements have been published by Tanuma et a12. The reliable experimental determination of the electron transport parameter is rather a complicated task. Among them the following methods are applied. The overlayer method which consists of depositing a thin film * This paper is dedicated to the memory of Prof Pierre Auger, deceased

December 24, 1993.

of material on the substrate followed by measurements of the attenuation of Auger electrons or photoelectrons. It provides the value of attenuation length (AL), which is derived from the overlayer film experiments on the basis of a model in which elastic electron scattering has been ignored. The distinction between terms characterizing electron transport such as IMFP and AL has been made in the standard proposed by the E-42 Committee of the ASTM3.4. The difference between AL and IMFP may reach 30%. Elastic peak electron spectroscopy’ (EPES) proved to be an efficient tool for experimental determination of the IMFP. It can be apphed for any solid smooth sample surfaces. The present work deals with the determination of IMFP by EPES applying the Monte Carlo analysis with the multiple electron scattering encountered. Special attention is paid to the quality of the sample surface. 2. Theory The theory relating the elastic backscattering probability and the IMFP6,’ has been described in detail in earlier publications. The crucial point is the proper choice of standard material. A number 591

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of IMFP and AL exhibiting a reasonable agreement should be available from the literature. In the present work values of IMFP for Ni standard in the energy range 500-2000 eV were taken from Tanuma et at, and above 2000 eV from Ashley and Tung8. Details of the Monte Carlo algorithm are described in ref 1. In the usual simulation scheme, the trajectories are assumed to consist of linear steps between elastic collisions, and the electron motion is approximated by the stochastic process. Elastic scattering events are modelled by the realistic differential scattering cross-section calculated from the partial wave expansion method applied to the Thomas-Fermi-Dirac potential. The electron history in the solid is pursued until the electron leaves the solid or until the total trajectory length becomes too long to give a noticeable contribution to the backscattered current. The Monte Carlo calculations are performed until the accuracy of the elastic backscattering probability within a given solid angle reaches the range l-2%. The necessary number of trajectories varies between 2 x lo5 and 2 x 106. Several papers have been published on the evaluation of IMFP by EPES9. The first attempt applied a single elastic scattering approach. Two methods have been used :

3. Sample preparation The surface quality of the sample is strongly affected by its preparation conditions. The average surface roughness r, was measured with a RHKIOO type STM, observing 500 x 500 nm area by InA. The measured value of rb is particular for the surface condition achieved by Ar ion bombardment. Each sample was prepared by a different method. Cu sample was prepared by electrolytic deposition on diamond paste polished and electropolished brass substrates (LORIX Ltd). Such a sample (with r, = 2 mu) is used as a reference material in quantitative surface analysis and spectrometer calibration. Ni samples have been prepared by vapour deposition, with a deposition rate of 1 rim/s on polished Si substrates in high vacuum at 100°C. Their thickness was 100 nm, with a roughness of rb = 1 nm at the surface. Ag sample was prepared by vapour deposition in high vacuum on polished Si substrate. The deposition took place at temperature 30°C with the deposition rate 1 rim/s resulting in a thickness of 100 nm. Roughness rh = 1.5 nm was found at the Ag surface. 4. Experimental

(i) Comparison of the elastic peak height’ of the sample with that of a reference sample of AI. (ii) Measurement of the elastic reflection coefficient of the sample with a retarding field analyzer (RFA) of large angular window”. The IMFP values for a number of elements were obtained using the effective elastic backscattering cross section’ and from differential scattering cross section”. Application of the multiple elastic scattering events Monte Carlo theory’2.‘3 and using the Al standard resulted in improved IMFP data although the discrepancies for high atomic number elements still occurred. Further step for improvement’4 was the spectrometer correction of the elastic peak which might be affected by the continuous background, adjacent to energy of primary backscattered electrons. A further development of EPES was published by Dolinski et ul”, using RFA for determining the absolute values of elastic reflection coefficient. The application of Monte Carlo analysis”.” resulted in good agreement of IMFP values for Ag and Au with theoretical values of Tanuma et al. The values for Cu were systematically 1ower’5. Reasonable agreement between the theoretical and experimental IMFP values for Au and Pt was obtained by Beilschmidt and Werner’h. The hemispherical analyzer (HSA) was used and the Al standard was replaced by Ni reference sample. New reliable IMFP values of Ni are available2,8 like those for AI. In fact, the Ni reference sample resulted in better agreement with Tanuma’s data than Al. The discrepancy of the results using the Al seems to be obvious. It can be attributed to two factors: the high background and loss spectrum adjacent to elastic peak. Another reason could be due to the surface roughness of the Al sample subjected to ion bombardment cleaning in order to remove the natural oxide surface layer. In the present work, Ni was used as the reference sample. The energy range was extended form 2 to 3 keV. The surface roughness of the Ni standard and the samples submitted to IMFP evaluation were determined by scanning tunnelling microscopy (STM). The surface cleaning by Ar ion bombardment was improved using Zalar rotation of the sample and optimized ion bombardment parameters, like glancing incidence of ionsI as well as suitable ion energy. 592

As received samples were mounted in the LJHV spectrometer and cleaned by Ar ion bombardment during rotation of the samples. Angle of Ar ion incidence was 4”, the energy 2 keV, the current 5 PA and the beam diameter 300 pm. The performance of the applied argon gun is described in ref 17. The cleaning procedure was verified by AES. The surface roughness of each sample was measured by STM (Res Inst Mt Sci, Budapest, Hungary). The AES and EPES were carried out in Res Inst Techn Phys, Budapest. AES and EPES spectra were acquired by computer, operating on line with Riber CPC 103 CMA ana1yzer5. The elastic peak intensity was measured in analogue mode. The CMA integral gun was operated under nearly normal incidence angle, with beam diameter 50 pm and current 2 PA. For every elastic peak recorded at different primary energy, a new freshly cleaned surface was produced by Ar sputtering, supplying the constant depth resolution of 3 nm”. The measurement of elastic peak intensity for every sample at given primary energy was referred to the same measurement at the Ni reference sample. Primary energy was varied between 500 and 3000 eV in 500 eV steps. Spectrometer corrections were applied according to ref 14 for both sample and Ni reference. 5. Results Results are summarized in the figures showing the calculated working curves of the elastic peak ratio Ix/l,, (corrected for the spectrometer) versus the IMFP as a free parameter. The measured intensity ratios are indicated for every energy by the horizontal line. On the abscissa, the experimental IMFP values obtained by the vertical line intercepts are denoted. The theoretical values are indicated by arrows, the Tanuma et aP data are denoted by P, and Ashley and Tung data by A. The figures represent the IMFP values versus energy for Cu and Ag. 6. Discussion In our previous paper, using Al as reference, the IMFP values exhibited systematically lower (73% for Au and 56% for Ta) values with respect to Tanuma’. Recently Beilschmid’6 using Ni reference,

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found 63% difference with respect to Al. This can explain the discrepancies of our previous IMFP data. Applying the correction factor for the Ni standard with respect to the Al reference, our previous data”, the results on Ta, W and Au, are in better agreement with Tanuma’s results. In Figure 1 on Cu with Ni reference, the agreement with Tanuma’ in the 0.52 kV, and with Ashley for 2-3 keV is very good. In Figure 2, good agreement was found for Ag with Ashley in the 2-3 keV energy range. In Figure 3 Tanuma’s results (extrapolating them above 2 keV)

are compared with our present experimental data on Cu (Figure 3(a)), Ta (Figure 3(b)), W (Figure 3(c)) and (Figure 3(d)) applying the correction factor 1.63 onto our previous results published in ref 13. The agreements are quite good. The deviations on Au can be attributed to the less good sample quality. It should be underlined, special attention was paid to the surface roughness, provided by ion sputtering procedure. Ni proved to be a suitable reference standard for measuring the IMFP. Reasonable agreement of IMFP values was found with RFA”,

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Figure 1. IMFP of Cu. master T&ma and Ashley, resp.

curve, exoerimental

results

and data

of

Figure 2. IMFP of Ag, master curve, experimental

results and Ashley’s

data.

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1000

1500 E W

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Figure 3. Comparison of Tanuma’s IMFP data (with extrapolation above 2 keV) with experimental results. (a) Cu, full line data of Tanuma and Ashley, resp ; (b) Ta, our previous Ta experimental curve corrected for the Ni/Al standard ; (c) the same for W ; (d) the same for Au. 593

G Gergely et al: Experimental

HSA16 and the present method.

CMA

determination

experiment,

by EPES

justifying

the EPES

Acknowledgements This research program has been supported by OTKA projects 1224 and T7694 by the National Scientific Research Fund of Hungary. Electrolytic Cu samples have been prepared by Dr J Loranth, LORIX Ltd, Budaors, Hungary.

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