Elastic backscattering of electrons: determination of physical parameters of electron transport processes by elastic peak electron spectroscopy

Progress in Surface Science 71 (2002) 31–88 www.elsevier.com/locate/progsurf

Elastic backscattering of electrons: determination of physical parameters of electron transport processes by elastic peak electron spectroscopy G. Gergely

*

Research Institute for Technical Physics and Materials Science, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary

Abstract This review paper is concerned with elastic peak electron spectroscopy (EPES) and information it gives on electronic transport phenomena. Experimental methods are described for determining the physical parameters such as the inelastic mean free path (IMFP), the life time of hot electrons, the elastic- and inelastic-scattering cross sections, the surface excitation parameter (SEP), etc. used by Auger electron spectroscopy, X-ray photoelectron spectroscopy, reflection electron energy loss spectroscopy, electron microscopy, etc. These quantities are associated with the elastic reflection coefficient re of the solid, appearing in the elastic peak Ie ðEp Þ. re is a material parameter, determined by E energy, Z atomic number and by the angular conditions. It is measured by EPES. Ie ðEp Þ is affected by the electron spectrometer parameters, such as energy resolution, angular conditions and the full width at half maximum of the electron source. The phenomenological properties of the elastic peak and the physical processes are presented, including subtle effects such as extended fine structure, recoil and refraction of electrons. Experimental problems are discussed including sample cleaning, surface layer amorphization, crystallinity effects, spectrometers, their calibration, reference standard samples, etc. Calculation methods for the relevant parameters and the evaluation of experiments (by Monte Carlo simulation) are briefly described. Applications of EPES for determination of the physical parameters (IMFP, the elastic- and inelastic-scattering cross sections, SEP) are briefly reviewed. Besides a compilation of the literature, some new results are presented.
2002 Elsevier Science Ltd. All rights reserved. Keywords: Elastic scattering of electrons; Physical parameters of electron transport processes

*

Fax: +36-1-275-4996. E-mail address: [email protected] (G. Gergely).

0079-6816/02/$ - see front matter
2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 7 9 - 6 8 1 6 ( 0 2 ) 0 0 0 1 9 - 9

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G. Gergely / Progress in Surface Science 71 (2002) 31–88

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Preparation of the sample surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Electron spectrometers used for EPES . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Electron microscopic EPES (SEM, SAM, STM) . . . . . . . . . . . . . . . . . . 2.4. Calibration of electron spectrometers for quantitative EPES . . . . . . . . . . 2.5. Reference standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Experimental parameters of the elastic peak. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. The elastic reflection coefficient and angular distribution of the elastic peak 3.2. The FWHM, energy distribution, position and intensity of the elastic peak 3.3. Morphological effects: diffuse media . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Elastic reflection of electrons on single crystal surfaces, diffraction, DEPES, channeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Temperature effects in EPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6. Extended fine structure of elastic scattering, EXFSEPES . . . . . . . . . . . . 3.7. Spin polarized elastic scattering, SPEPES . . . . . . . . . . . . . . . . . . . . . . . 4. Physical processes in elastic backscattering of electrons. . . . . . . . . . . . . . . . . . . 4.1. Electron impact and SEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Refraction of electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Very low energy loss processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Surface excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Elastic scattering of electrons: differential elastic-scattering cross sections . 4.6. Single and multiple elastic scattering of electrons: ke and ki IMFP . . . . . 4.7. Life time of hot and medium energy electrons . . . . . . . . . . . . . . . . . . . . 4.8. Escape of the electron from a solid surface . . . . . . . . . . . . . . . . . . . . . . 5. Calculation of elastic reflection of electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. The layer model with single-scattering approach . . . . . . . . . . . . . . . . . . 5.2. Monte Carlo (MC) simulation in EPES . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Analytical solution of the electron transport equation . . . . . . . . . . . . . . 6. Determination of physical and material parameters by EPES . . . . . . . . . . . . . . 6.1. The differential elastic-scattering cross sections drðE; Z; hÞ=dX of electrons 6.2. Experimental determination of IMFP ki . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Determination of the inelastic-scattering cross section of electrons. . . . . . 6.4. Determination of the surface excitation parameter . . . . . . . . . . . . . . . . . 6.5. Determination of the cross section for electron induced desorption (EID) 7. An outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34 38 38 40 42 42 47 49 49 52 56 58 59 59 60 60 60 61 62 63 64 67 69 70 70 70 70 72 73 73 74 78 78 80 81 82 83

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Nomenclature AES Auger electron spectroscopy ARAES angular resolved AES AREPES angular resolved EPES ASTM American Society for Testing and Materials CMA cylindrical mirror analyzer CRR constant retarding ratio DAES directional AES DAPS disappearance potential spectroscopy DDF depth distribution function DEPES directional EPES EELS electron energy loss spectroscopy EID electron impact desorption EPES elastic peak electron spectroscopy EXFSEELS extended fine structure EELS EXFSEPES extended fine structure EPES FWHM full width at half maximum HREELS high resolution EELS HSA hemispherical analyzer ID information depth ISO International Standard Organisation IMFP inelastic mean free path LEED low energy electron diffraction LEEELS low energy EELS MC Monte Carlo ML monolayer NIST National Institute for Standards and Technology NPL National Physical Laboratory PSL porous Si layer PWEM partial wave expansion method REELS EELS in reflection mode RFA retarding field analyzer SAM scanning Auger microscopy SEE secondary electron emission SEM scanning electron microscopy SEP surface excitation parameter SCPEELS scanning probe EELS SPEPES spin polarized EPES SPLEED spin polarized LEED SPM scanning probe microscopy STM scanning tunneling microscopy UHV ultrahigh vacuum

33

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UPS XPS

ultraviolet photoelectron spectroscopy X-ray photoelectron spectroscopy

1. Introduction Electron spectroscopies are widely used in surface science for both determination of surface structure using diffraction techniques such as LEED, and for determination of surface composition by measuring emission of electrons with characteristic energies as is done in for instance XPS or AES. The latter two techniques have recently been reviewed in [1]. For diffraction techniques elastic scattering is used, but for elemental analysis emitted electrons are generally studied. The rather large fraction of elastically scattered electrons is in many experiments completely ignored. Surface analysis using those elastically backscattered electrons is the topic of the present Progress report. The research is focused on the peak of the energy and angular distributions of the elastically scattered electrons, hence the name elastic peak electron spectroscopy (EPES). Knowledge of the transport of electrons through solids and their mean free paths is essential to EPES, and these topics have been reviewed recently as well in [1,2]. Werner [4] specifically reviewed electron transport in solids for surface analysis. Together with Refs. [5,6], these reviews cover the state of the art of theory and experiment of electron spectroscopies at surfaces by techniques such as XPS, AES, UPS, and REELS. The present review paper will be a continuation of the theoretical review papers concerned in part with EPES [2–4], complementing them from an experimental perspective. Its goal is to present experimental methods for determining the physical parameters discussed in [1–4] (the IMFP, the elastic- and inelastic-scattering cross sections, surface excitations). Many contradictory results have been published on physical parameters derived from EPES experiments. Their experimental verification is very important. The reliability of the theoretical methods and models requires experimentally verified input parameters and simulation procedures. The present report will provide experimental information. The intensity and angular distribution of emitted electrons is determined by electron transport processes in all types of electron spectroscopy and microscopy such as AES, XPS, UPS, REELS, EPES, SEM, or SAM. The relevant physical parameters are: the inelastic mean free path (IMFP) [7], the transport mean free path [3], the life time of hot electrons [8], the differential elastic- [9] and inelastic-scattering cross sections [10] and the surface excitation parameter (SEP) [11]. These parameters determine the elastic backscattering of electrons and they appear in expressions for the elastic peak intensity. EPES [12] deals with the experimental determination of electron elastic backscattering. The last review paper in this field has been published by Nakhodkin and Melnik [13] in 1994. Since this time, a great number of new results have been

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published. EPES can be applied to any atomically clean, flat solid surface of elements and compounds. The present work covers the medium energy range E ¼ 0:1–5 keV. Elastic scattering is dominated by electron–atom interactions, and the elastic peak is the largest peak in the electron spectrum. EPES is an auxiliary method of AES and REELS, and is also applied in electron microscopy (SEM, SAM, STM). The elastic peak can be used as an internal reference peak for AES–SAM, REELS and even SCPEELS [14]. Powell and Jablonski [7] (the US National Institute for Standards and Technology (NIST)) recommend the application of EPES for the measurement of the IMFP. The IMFP is an important materials parameter because it determines the information depth of AES, XPS, SEM, SAM, photoemission microscopy and REELS. The IMFP is determined by the life time and energy of hot electrons [8]. In some cases, the giant elastic peak signal supplies additional information for AES or XPS and electron microscopy. REELS is quantified by the elastic peak. The inelastic-scattering cross sections are deduced from REELS measurements, based on the elastic peak [6]. Surface electronic excitations reduce the intensity of Auger and photoelectrons and of the elastic peak as well. The only experimental possibility for measuring the SEP is offered by the elastic peak. Some special effects such as the recoil effect [13], spin polarization [15], extended fine structure and electron refraction [13] are revealed by the elastic peak. Reliable determinations of the physical parameters for electron transport processes have to be taken into consideration for a satisfactory description of elastic backscattering of electrons. The elastic scattering of electrons by solid surfaces is a phenomenon studied since the classic Davisson–Germer experiment of LEED. Considerable experimental and theoretical work has been made on elastic-scattering phenomena, and some pioneering studies are cited in [12]. Conventional EPES deals with incoherent elastic scattering of electrons on a disordered, amorphized surface layer, thereby avoiding crystalline and diffraction effects [16]. Some coherent scattering phenomena and crystalline effects will be considered in this review paper. Elastic electron-scattering is responsible for the elastic peak Ie ðEp Þ, and is associated with the strong, long-range electron–atom interaction. Ie ðEp Þ is a strong function of Ep the energy of the primary electrons, of ai the angle of incidence and of ad the detection, (both measured with respect to the surface normal), the target material, particularly its surface composition and its morphology. The measured FWHM DEe of the elastic peak is determined by the energy resolution DEs of the analyzer, by the recoil effect (described later) and by the FWHM DEg of the electron source. The elastic current ie ðEÞ is measured with the spectrometer at E ¼ Ep as a function of scattering angle. The elastic peak signal Ie ðEp Þ ¼ ie ðEp ÞRðEp Þ is the emitted electron current ie ðEp Þ as detected by an analyzer with the response function RðEÞ. The latter function is the product of the analyzer transmission function T ðEÞ and detection efficiency DðEÞ. The elastic reflection coefficient res ðEp Þ within the spectrometer angular aperture is given by the ratio of the current of emitted elastically scattered electrons ie ðEp Þ and the primary current ip : res ðEp Þ ¼ ie ðEp Þ=RðEÞip

ð1:1Þ

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Fig. 1. IðEÞ spectrum of secondary and backscattered electrons for a Cu sample [18]: Ep ¼ 1800 eV; EA ¼ 916 eV; the Auger peak energy, DEe ¼ 2:4 eV.

In Fig. 1, a typical electron energy spectrum on a Cu sample [17] is presented, obtained with a HSA described in [18] with ai ¼ 20 and ad ¼ 40. In Fig. 2, the elastic peak spectra with adjacent loss spectra IðEL Þ for Si are compared for two electron spectrometers with different energy resolutions: a CMA Riber OPC 103 and a HSA ESA 31 [19], measured at Ep ¼ 1 keV. They are strongly affected by the energy resolution. The intensity scales are individually normalized. In our first EPES experiments a CMA was applied. It is used in many laboratories nowadays. In conventional AES, the elastic peak is used merely for optimizing the sample position [12]. EPES measures the elastic peak signal. The following notations and parameters will be used: • Ie ðEp ; ai ; ad ; DXÞ. The angular range of ad determines the solid angle of detection DX of the analyzer. • re ðEp ; ai ; ad ; DXÞ is the elastic reflection coefficient of the surface, in most cases for ai ¼ 0 is used (normal incidence). • Working with a spectrometer of small DX and variable ai or ad , Ie ðE; h; DXÞ is the angular distribution of the elastic peak for a scattering angle h (measured from the incident beam direction). This is shown in Fig. 3. DX is determined by Dad . • res ðE; h; DXÞ (%) is the angular variation of the elastic reflection coefficient with h, for specified E measured within the spectrometer angular acceptance window DX. Many experiments are based on H. • dre ðEp ; hÞ=dX is the differential elastic reflection coefficient for energy Ep and scattering angle H. The NIST databases have been prepared with H. The elastic reflection coefficient data res ðE; Z; ai ; ad ; DXÞ for an element with atomic number Z, convoluted with the angular conditions and instrumental parameters of the spectrometer, particularly RðEÞ and the energy resolution, are material

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Fig. 2. Comparison of EPES Si measured by a CMA (broken line) and with the ESA 31 HAS (full line) Ep ¼ 1 keV.

Fig. 3. Experimental arrangement for AREPES notations: 1 sample; 2 Faraday cup; 3 electron gun; 4 electron spectrometer, rotable with ad ; Dad is the angular window of the analyser; H is the scattering angle.

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parameters. The res ðE; Z; ai ; ad ; DXÞ data also depend on characteristic material parameters, such as the IMFP and the differential elastic-scattering cross sections, to be discussed in this review.

2. Experimental methods 2.1. Preparation of the sample surface The experimental techniques for EPES are similar to those of other electron spectroscopies in surface analysis. A review of the methods, instruments and procedures is given in the Handbook of Briggs and Seah [20]. EPES spectra are measured in UHV, <107 Pa pressure range, ideally on atomically clean surfaces. These are prepared by ion bombardment cleaning, in most cases with Arþ ions. Conventional Arþ bombardment produces clean and rough surfaces. The problems of Arþ sputtering are discussed in [20, Chapter 4] and [21,24]. Roughening [21–23] was successfully eliminated by Zalar rotation [25] of the sample and by using a dedicated device with glancing incidence of ions [26]. In some special cases, ion bombardment can smooth a rough surface [23,24]. With a dedicated device a depth resolution of 2 nm was achieved after removing a surface layer 500 nm thick [24]. Another effect of ion bombardment is the amorphization of the surface layer [24,27,28]. The thickness da of the amorphized layer is given by the expression [28] da q ¼ Ai Eion cos adi

ð2:1Þ

In Eq. (2.1) q is the density of the sample, Ai is a material constant, Ai ¼ ð1–1:4Þ  106 for semiconductors Si, Ge and GaAs. Eion is the energy of Arþ ions, adi their angle of incidence with respect to the sample normal. In Fig. 4, an XTEM micrograph of Si is shown [24] prepared by sputtering with Eion ¼ 250 eV, in Fig. 5, a similar micrograph is shown for Eion ¼ 3 keV. They show the amorphized surface layer and also the surface roughness after sputtering. The XTEM sample was prepared by depositing a thick film of Al on the amorphized surface [24], thus forming a sandwich structure. Amorphization of the surface layer is generally necessary to avoid crystallinity effects [16]. In our earlier work [12] no difference was found in the elastic peak intensities measured on semiconductor single crystals Si or on polycrystalline Si surfaces, cleaned by Arþ ions. This result is specific for the material, electron and ion energy and experimental configuration. The surface roughness after ion sputtering can be checked by STM [17,21,29]. Any residual contamination of the sample surfaces is checked by AES or XPS. The surface is considered atomically clean if no impurities are observed by AES or XPS (O or C peak <1%). During prolonged measurements, the recontamination of the sample can take place from the residual gases (particularly H2 O, CO) in the vacuum system. This possibly must be checked and the surface cleaning repeated if necessary. In some cases as-received samples (e.g. porous Si, polymers, etc.) are introduced into the vacuum chamber. Clean Si surfaces can be prepared by HF treatment producing

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Fig. 4. XTEM image of Si amorphized by 250 eV ions, da ¼ 2 nm.

Fig. 5. XTEM image of Si amorphized by 3 keV Arþ ions, da ¼ 7 nm.

a Si–H stable surface bond. H is not observed by AES or XPS and the adlayer will be desorbed when baking the UHV system [30]. Polymers and organic compounds are

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sensitive to electron impact [31], which can lead to fragmentation; precautions are needed, by reducing the ion current density and bombarding time. The surface composition should be checked during cleaning. This will be discussed in Section 6.2. A special problem is the surface cleaning of binary compounds, metal alloys or compound semiconductors or insulators. Due to the variable sputtering rates of the constituents (e.g. GaAs, InP, etc.), enrichment of the metallic constituent occurs in the surface layer [32,33]. In binary alloys, segregation can take place. In insulators (SiO2 , Si3 N4 , etc.) the O or N is partly desorbed, thereby producing deviations from the initial stoichiometry. All of these effects might affect the elastic peak intensity, due to the altered composition in the surface layer. The real surface composition can be determined by AES or XPS [34] and taken into consideration in the evaluation of EPES experimental results [35]. The best solution of the problem is the reconstruction of stoichiometry. This was done by MBE for GaAs in EELS experiments [36]. Another possibility is the production of the compound crystal surfaces by cleaving, followed by EPES measurements. No such work has been published as yet. Alloy surfaces can be annealed but surface segregation of one component could still be a problem. 2.2. Electron spectrometers used for EPES In the Handbook [20] a review is given in Chapter 2 on instrumentation and most important spectrometers are discussed. Here a brief review is given with the respect to EPES applications. The most important electron spectrometers are summarized in Table 1. The retarding field analyzer (RFA) is a suitable tool for measuring res ðE; ZÞ in percentage units [37–39]. A special RFA was described in [40], in which the backscattered intensity of electrons was integrated over a hemisphere, an ideal situation for the measurement of reHS . The latter denotes the elastic reflection coefficient for a hemisphere, but no such experiments have been published as yet. The RFA can be operated in analogue (measuring the current of electrons retarded by E) or in derivative mode, using phase sensitive detection. The first harmonic represents the energy spectrum of electrons and for E ¼ Ep the elastic peak.

Table 1 Electron spectrometers Analyzer

ai ()

ad ()

E (eV)

DEs

Mode

Reference

RFA

0

5–75, 0–90

50–1500

0.8%

AC–DC

[20,37–40]

CMA

0 0

42.3  3.5 42.3  6

50–3000 1–5000

0.25–0.45% 0.25%

AC–DC DC

[20] [41]

HSA ESA 31

Arbitrary 50

Arbitrary 04

50–2000 10–10000

Good 50–2600 meV

Arbitrary DC–FRR

[18,20] [19]

DESA-100

0

19–29

100–2500

0.1–2 eV

DC

[42]

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The cylindrical mirror analyzer (CMA) is widely used in AES. An improved version is the double pass CMA (DCMA) [20]. The most advanced CMA was developed by Goto et al. [41] enabling the measurement of the primary electron beam current with a Faraday cage mounted in the sample holder. This CMA supplies absolute values for res . In general the CMA is operated in analogue (direct current) [41] or derivative mode (rather for AES). In most cases ai ¼ 0. The hemispherical analyzer (HSA) has a good energy resolution DEs but a small acceptance angle. It is mainly used for XPS. Many types of HSA are available, and they are operated with different angular arrangements and energy ranges. In our EPES studies with a HSA, the ESA 31 was used [19], operated in pulse counting mode. A combination of the RFA and CMA was described by Staib and Dinklage [42]. It was realized with the Riber and Cameca MAC3 and a new high performance version is available as the DESA 100 from Staib Ltd. The distribution Ie ðE; Ep Þ of the elastic peak is affected by DEs and by DEg (FWHM of the electron gun). In Fig. 6, the elastic peak distributions are compared for different values of DEs , as measured with the DESA 100. The FWHM of the elastic peak is strongly affected by the energy resolution, its choice however is a compromise with the intensity requirements. All electron spectrometers for EPES need a primary electron gun. Several types are available differing in the beam current and energy. The most important parameter for EPES is DEg . It is determined by the Boersch effect [12,43], the cathode temperature and the electron optical system. Some experimental values are: 0.4 eV for the ESA 31, 1.1 eV for the DESA 100 and 0.5 eV for GotoÕs CMA. Several types of electron spectrometers have been developed for the measurement of the angular distribution Ie ðE; hÞ of the elastic peak intensity or of the elastic reflection coefficient dre ðEp ; hÞ=dX. These spectrometers are described in the references in Tables 3 and 4 [37,38,45–52]. A typical experimental arrangement [45] is shown in

Fig. 6. The variation of the elastic peak FWHM DEe of Ag with DEs spectrometer resolution at Ep ¼ 1 keV. Ie ðEp Þ is presented in arbitrary units, but normalized to the same intensity at the peak maximum.

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Fig. 3. Oguri et al. [50] used a movable 127 cylindrical condenser analyzer and a movable primary electron source monochromatized with another analyzer, in the range h ¼ 20–110 and E ¼ 50–500 eV. Hoffmann and Sanz [20,52] mounted a rotable transmission slit in a DCMA. The most advanced device has been elaborated by Fink [45]. The operating parameters are E ¼ 600–2000 eV, h ¼ 110–160, DEs ¼ 0:8–1:5 eV at E ¼ 2 keV. The elastic peak signal, i.e. the intensity Ie ðEp Þ detected by the spectrometer is measured for a specified incident current. This signal can be measured in analogue mode with an electrometer [41], or by using an isolation amplifier [53]. Nowadays many electron spectrometers are operated in the pulse counting mode using a channeltron detector [54]. The derivative mode supplies Ie0 ðEp Þ from modulation of the analyzer pass energy in for example a CMA or HSA and detection of the first harmonic [55]. In that case, Ie ðEp Þ can be obtained by integrating I 0 ðEÞ. In the RFA analyzer the first derivative of the detected signal supplies the electron spectrum IðEÞ, the second derivative gives I 0 ðEÞ. EPES studies with the RFA are made in the derivative mode (first harmonic) [55]. Gruzza et al. [56] used the integrated high-energy side of the elastic peak produced by the RFA signal IðEÞ to minimize problems caused by the overlap of the elastic peak with the energy loss spectrum for the relatively large energy resolution (DEs ¼ 0:008E) of their analyzer. In the past CMA analyzers used for AES worked in the derivative mode. Nowadays differentiation of the analogue spectrum with a computer is preferred. Such differentiation can be conveniently accomplished using the Savitzky–Golay algorithm. 2.3. Electron microscopic EPES (SEM, SAM, STM) In general, the electron spectrometer can be operated as part of a microscope if the electron gun produces a finely focused beam, like that for scanning Auger microscope (SAM) [20]. The conventional SAM analyzers however are confined to the AES, XPS energy range E < 2:5 keV. A high performance SAM system was elaborated by Prutton et al. [57] designed also for EPES. Seiler [58] and Boengeler et al. [59] published reviews that describe problems of low-energy electron microscopy including EPES. Schmid et al. [37] used the elastic peak for imaging with a scanning electron microscope (SEM), varying the sampling (information) depth ID with Ep . ID is defined in the ISO 18115 Standard (No. 5.170). ID for EPES will be discussed in Section 5.2. Very recently elastic peak measurements with plasmon loss spectra have been determined in a STM combined with REELS [14]. 2.4. Calibration of electron spectrometers for quantitative EPES Abundant literature is available on the calibration of electron spectrometers. Here only the Handbook [20] is mentioned as a guide to this literature: ASTM Standard E1016 [60] specifies instrument parameters that affect the elastic peak intensity IðEp Þ. These parameters are: DEs ðEÞ the energy resolution, T ðEÞ the transmission, DðEÞ the detection efficiency, the angular conditions (ai , ad , DX angular window) and the

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energy range. A lot of work has been published on quantitative EPES, working with these instrument parameters when evaluating experiments. In the following, a brief review is given on the experimental determination of the main instrument parameters, using different methods for various types of analyzer, but the type of signal also might be important. Abundant literature is available on the calibration of the energy scale [20,61,62], mainly dealing with calibration for XPS, since the exact knowledge of the peak position is needed for the binding energy measurements. The energy calibration of Auger spectrometers has been elaborated by NPL [61]. More precise studies revealed the importance of the recoil shift [63], the role of the work function of the analyzer [64] and of the electron gun [65]. The energy scale in EPES is determined by the calibration parameters given by the manufacturer of the spectrometer. For a CMA E ¼ ECMA  1:6. ECMA corresponds to the voltage applied on the CMA electrodes. The electron trajectories are affected by relativistic effects [66,67] and the energy position is shifted by 2–11 eV between E ¼ 2–5 keV [65,66]. In practice for EPES of medium energy electrons, the energy of the elastic peak can be taken to be identical to its nominal value. The relative elastic peak positions (recoil shifts) however might be important; this effect will be discussed later. The relativistic effects are important for CMA or DCMA spectrometers, however for HSA type analyzers in which electrons are decelerated, they can be neglected. The calibration of the electron spectrometer response RðEÞ can be based on backscattering spectra [53]. Continuous IðEÞ spectra and ie elastic current values have been published by Goto et al. for Si [66], Ni [68,69], Au, Ag, Cu [70] and for C [69,71] for ip ¼ 1 lA. Standard spectra determined by Goto are available upon request. The NPL (National Physical Laboratory, Teddington, UK) developed a system and software for spectrometer calibration based on measurements of Cu, Ag and Au for specified conditions [72]. Intensity calibration in absolute units is suitable for HSA and CMA spectrometers and was used for AES. Intensity calibration can be based on the IðEÞ spectra of Goto [68–71], but the effects of energy resolution (DEs ) should be taken into consideration. Absolute res ðE; hÞ AREPES data are available in the theses of Fink [45] and Koch [74]. The intensity calibration of the ESA 31 [19] and the DESA 100 spectrometers is described in [75]. The RFA supplies absolute values of res detected within DX. Its calibration is described in [37,38]. The T ðEÞ and DEs ðEÞ characteristics were determined by analysis of the collected current versus various gun parameters. They should be used for evaluation of RFA experiments and corrections for energy resolution are absolutely necessary. Another method was elaborated by Gruzza et al. [56] working with the high-energy side of the elastic peak. A practical method was developed by Mroz et al. [76], in which the primary electron beam was deflected to the collector by a retarding field produced by a bias voltage on the sample. Thus knowledge of T ðEÞ is not necessary, since the ratio ie ðEp Þ=ip ¼ res ðEp Þ, can be obtained from two measurements under the same conditions. Bideux et al. [77,78] improved the method of Mroz by optimizing the bias voltage and comparing the high-energy side of the elastic peak (E > Ep ) from the sample to that of the deflected beam. Except at very low E values

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(E < 100 eV), the poor energy resolution of the RFA strongly distorts the EPES spectra [39], and a spectrometer correction is needed [79,80]. The RFA integrates the IðEÞ spectrum adjacent to Ep and affects even the high-energy side of IðE; Ep Þ. On the other hand, the deflected primary beam represents the Boersch width [43] of the electron gun DEg broadened by DEs . According to [81] the energy distribution of the electron gun can be approximated by a Gaussian, with the energy distribution of the elastic peak defined by a Gaussian width parameter re ¼ 0:6DEe , and the intensity IðE; Ep Þ is given by 2

IðE; Ep Þ ¼ Ie ðEp Þ expfðEp  EÞ =r2e g

ð2:2Þ

The measured FWHM of the elastic peak DEe is affected by DEg of the electron gun. The elastic peak is also broadened by the recoil effect [82] and by very low energy phonon losses (<50 meV). In practice, these broadenings are not very significant. According to experiments and Eqs. (2.2) and (2.3) an IðE; Ep Þ signal is observed even for E > Ep . Let us consider two extreme cases: (1) DEs  DEg , then the measured elastic peak distribution mainly reflects that of the electron gun. IðEp Þ ¼ Io DEs . The elastic peak intensity shows linear relationship with DEs . No distortion occurs in the spectrum [83]. (2) DEs DEg , DEe is determined by DEs , and strong broadening of DEe occurs. The distribution of the spectrum IðEp ; EÞ is given by Eq. (2.2), and a spectrometer correction is essential [80,83]. As shown in [81], the measured elastic peak intensity is given by DEs IðEp Þ ¼ IDEe qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DEg2 þ DEs2

ð2:3Þ

Eqs. (2.2) and (2.3) refer to narrow peaks such as like Auger or elastic peaks. This is not the case for the continuous background Ib ðEÞ or a slowly varying IðEÞ. The physical background Ib ðEÞ is determined by the backscattering spectrum [53], produced by inelastic-scattering processes. As shown in [81] the intensity of the continuous background Ib ðEÞ exhibits linear relationship with DEs . The background thus increases with DEs . This relation was verified by experiments [81]. The FWHM DEe of the elastic peak is determined byqDE s , DEg [43] and DER ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

(intrinsic recoil broadening) [63,82] resulting in DEe ¼

DEg2 þ DEs2 þ DER2 . The

validity of this relationship was verified in [83]. This relationship offers a possibility for estimating DEg based on knowledge of DEs . The measurement of DEg needs a spectrometer of very good resolution (DEs < 100 meV). A practical method is to decrease Ep until the analyzer resolution DEs becomes 100 eV). This analysis resulted in DEg ¼ 0:5 eV. In reality, neither the spectrometer energy window nor the electron gun lineshape is strictly Gaussian, as verified by experiments with the ESA 31 spectrometer [19,83].

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45

The experimental determination of the analyzer DEs ðE; E0 Þ energy window distribution function is difficult. A possible method is to use a monochromatized primary source, as done by Oguri et al. [50], but this method was limited to low E < 500 eV. The manufacturers communicate DEs ðEÞ of the CMA or HSA spectrometers for practical operating conditions. For a CMA DEs ¼ const  E. DEs ðEÞ of the HSA or DESA 100 can be varied by changing the retarding ratio. DER will be discussed in Section 6.2. The calibration of a CMA is a delicate problem. Calibration procedures have been elaborated for RðEÞ, T ðEÞ and DðEÞ by several authors [20,41,72,73,84]. In [51] a calibrated Cu standard was applied and the linear relationship of DEs with E was verified. Lysenko et al. [84] elaborated a method using square wave modulation. Abundant literature is available on the calibration of HSA spectrometers. The system of Seah [72] is useful also to HSA. Gruzza et al. [85] used a graphite standard sample and calibrated a HSA with the elastic peak of C. Ie ðEp Þ was calculated by Monte Carlo method. Hughes and Philips [86] used a small electron gun for calibration. Comprehensive works are presented by Schaerli et al. [87] and Osterwalder et al. [88] on HSA spectrometers, operated in CRR (constant retarding ratio) or CAE (constant analyzer energy) mode. The ESA 31 [19] and the DESA 100 spectrometers have been calibrated in our laboratory using Ni reference spectra [69,75]. The RðEÞ spectra are presented in Figs. 7 and 8. The transparency Tr of a CMA or RFA is constant, T ðEÞ ¼ Tr DEs . A possibility for determining it is an optical measurement [41,89]. Another possibility is given by the use of reference EPES standards, calculation of the relevant res values [74] and

Fig. 7. Comparison of the IðEÞ spectra of the ESA 31 with the CMA spectra of Goto, measured on Ni. Ep ¼ 2 keV. The ESA 31 was operated in the CRR mode, DEs ¼ 0:00022E. In GotoÕs CMA DEs ¼ 0:0025E. The ratio (in arbitrary units) is proportional to RðEÞ for the ESA 31. With the courtesy of Prof. K. Goto (Nagoya University) and the Surface Society of Japan.

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Fig. 8. Comparison of RðEÞ spectra of the DESA 100 and the ESA 31 (Fig. 7) at Ep ¼ 2 keV. The resolution DEs ¼ 200 meV, identical for both spectrometers. The operating angles are indicated in Table 1.

comparing them with GotoÕs spectra. Tr of GotoÕs CMA was estimated to be 20% [75]. Regarding DðEÞ, it is determined by the channeltron [54] or multiplier characteristics (communicated by the manufacturer) and by the electronic system as well. The spectrometer should be operated in the linear range or corrections are needed. Schaerli and Seah elaborated a method for DðEÞ correction [87]. Except for the measurement of res with a RFA, knowledge of T ðEÞðDðEÞ is not required for EPES. This difficulty was eliminated by deflecting the primary electron beam [76–78]. The CMA and HSA EPES experiments can use a reference standard. The accuracy of EPES experiments is determined by several factors, such as: • The stability of the atomically clean surface of the sample with respect to contamination from the residual gases in the chamber, such as CO, H2 O, etc. or by ion bombardment. • Contamination of the analyzer by residual gas or ion bombardment. • The stability of the detector and electronic system, e.g. drift in gain of the channeltron. • Precision of the electronic equipment. Goto [41,65,89,90] gives detailed data on his system, including noise and optimization of the electrometer detector system. For the energy measurements he used a high voltage divider (0.01%), calibrated using a voltage standard. The primary energy and current were set 5 keV (0.01%) and 1 lA (1%), respectively. For detection he used a Faraday cup of 99% efficiency. The ghost spectra were 103 of the elastic peak. • Sample position as discussed by Goto [65,66]. Working with the ESA 31 spectrometer, 1% reproducibility of EPES experiments was achieved, but during lengthy measurements, the repeated cleaning of the sample

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47

surface was sometimes needed [83]. The surface was checked before each measurement of the electron spectrum. Fink [45] also discussed the sources of error in EPES experiments. Except for spectrometers of very good DEs , resolution correction of the elastic peak is needed, which is material dependent [80]. The energy window of the spectrometer integrates the loss spectrum adjacent to Ep . This was verified by EPES experiments with different spectrometers [83]. Even the high-energy side of the elastic peak E > Ep can be distorted. Working with a CMA of poor DEs , quantitative EPES was based on the corrected elastic peak intensity and not on the peak area [12,91]. Using a spectrometer of good resolution [83], the integrated elastic peak area represents the number of elastically scattered electrons detected by the spectrometer. Quantitative EPES operated with a reference standard is based on the integrated peak areas of sample and standard. The same is valid for poor DEs spectrometers, using background subtraction of the elastic peak. Recently Tougaard et al. [92] elaborated a procedure for this purpose. HSA spectrometers operated at DEs < 200 meV and with DEs  DEg do not need correction. Quantitative EPES with a RFA needs spectrometer correction even working with the beam deflection method [76– 79]. 2.5. Reference standards The RFA can supply absolute values of res , for specified values of ad1 and ad2 , provided that spectrometer correction for energy resolution is applied [80]. The elastic peak can be used as an internal standard for AES or EPES. res data are presented versus E in [37,38,45,68–71,74,93–95] for some elements. Fink [45] and Koch [74] published res data for a number of elements. They indicated also reHS elastic reflection coefficient data, integrated for 2p solid angle and based on Monte Carlo analysis and ki IMFP data. The same works published also the angular distributions dre ðh; EÞ=dX. These data are suitable reference standards, due to the good DEs of their angular analyzer. Integration of dre ðE; hÞ=dX supply the res values in [45,74]. Goto published absolute values of reCMA for C [69,71] and Ni [68,69]. Using the spectrometer correction for GotoÕs experimental results, absolute values of reCMA can be deduced for re ðE; 138Þ. However, this requires the knowledge of the transmission Tr and the correction of EPES spectra for energy resolution, which are not available. It is interesting to compare GotoÕs data on C and Ni with those of Fink and Koch, and applying the angular acceptance window of 0.88 sr of GotoÕs CMA. The transmission Tr of GotoÕs CMA was determined in [65]. In [12] the absolute values of the elastic peak were deduced from the integrated IðEÞ electron spectrum. The backscattering coefficient rb (elastic þ inelastic) [53] is given by Eq. (2.4), it can be deduced from the electron spectrum corrected by RðEÞ response function of the spectrometer: Z Ep IðEÞ dE ð2:4Þ rb RðEÞ 50

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The elastic reflection coefficient measured with the same spectrometer was deduced from the elastic peak intensity: res ¼

fa Ie ðEp ÞDEg RðEÞrb

ð2:5Þ

fa is a correction factor for angular distribution of elastic/inelastic backscattering. In general, the inelastic backscattering on a solid surface shows cosine distribution, whereas the angular distribution of the elastic peak is Z and E dependent. rb is a material parameter determined mainly by Z. In the literature reliable rb data are available, August and Wernisch [96] summarized the previous results in the literature and published practical formulae for rb ðE; ZÞ. The knowledge of DEg and DEs is needed. In most cases, quantitative EPES compares the integrated elastic peak signal Ies ðEp Þ with that of a reference sample Ier ðEp Þ, in terms of their ratio Ies ðEp Þ=Ier ðEp Þ. In that case the spectrometer parameters T ðEÞ and DðEÞ are not needed, provided that Ies and Ier are corrected [92]. Turning to quantitative electron spectroscopy: AES and XPS are based on reference standards such as Ag [73,97], Au and Cu [17,68,70,73,89]. In addition, for EPES a problem is that angular distributions for Au and Ag are strongly varying with E [74]. Ag has a low energy loss peak (EL ¼ 3:8 eV) [98], not resolved by a typical CMA [80]. Using a spectrometer of very good DEs , Ag can be a suitable reference sample. It is a noble metal, less affected by residual gas than Ni. The strong broadening of Ie ðE; Ep Þ of Cu [17] and the plasmon loss structure of Al are disadvantageous for EPES. Cu might be a suitable reference sample using a spectrometer of very good DEs . Regarding C as a reference sample, precautions are needed. The reCMA ðEÞ (%) experimental data are different for graphite [69] and soot [71] respectively. The other problem is the angular distribution re ðE; hÞ of graphite. As found by Fink [45], above E > 800 eV and h > 110 the angular spectra of graphite are nearly constant versus h and do not obey the cosine distribution. The re ðhÞ at E ¼ 1000 eV was affected by the surface roughness, sputtered or polished graphite sample. Ni proved to be a practical reference sample for determining the IMFP ki by EPES [99,100] and recently also for quantitative EELS [83]. Its preparation and surface roughness have been described in [17]. Many data on Ni with relevance to EPES have been published in the literature: AES [68], EPES and total energy distribution [69], AREPES [74], experimental IMFP [100], phonon loss spectra [101], angular distribution [102], calculated IMFP [103,104], and surface phonons [105]. In Fig. 9 a typical Ni spectrum is presented, measured with the ESA 31 [19] at E ¼ 3 keV and DEs ¼ 200 meV. The REELS spectra are strongly affected by the DEs resolution. The IðEL Þ spectrum of Ni exhibits two important parameters [83]: the ratio rmax ¼ IðEp Þ=IðEL max Þ, i.e. that of the elastic peak with the maximum of the loss spectrum measured at EL max ¼ 26 eV, and rmin ¼ IðEp Þ=IðEL min Þ, i.e. with the minimum between Ep and the loss spectrum. Below DEs < 200 meV rmax and rmin are constant [83]. Some typical values for Ni and the ESA spectrometer are: rmax ¼ 85, rmin ¼ 95. Contamination of the Ni surface from the residual atmosphere decreases

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49

Fig. 9. IðEÞ spectrum of Ni measured with the ESA 31, Ep ¼ 3 keV. The REELS spectrum of Ni is also indicated on magnified scale.

rmax and rmin . Before Aþ etching rmax ¼ 25 and rmin ¼ 55 were found. Their values are characteristic for an atomically clean surface. They should be monitored during prolonged measurements [83]. To avoid crystalline effects [16], a microcrystalline Ni sample is needed. The electrolytic Ni described in [17] fulfills this requirement. At present the application of an Ag reference sample for EPES is preferred. Abundant literature is available on the physical parameters of Ag, such as those on Ni [70,74]. According to our last experiments, a-Ge (amorphous) seems to be a potential reference sample. This will be discussed in Section 6.4.

3. Experimental parameters of the elastic peak 3.1. The elastic reflection coefficient and angular distribution of the elastic peak Standardless quantitative EPES is based on two experimental parameters: res ðE; ai ; ad ; ZÞ, i.e. the elastic reflection coefficient of electrons measured on a clean surface under defined angular conditions and spectrometer parameters. Electrons are detected within the analyzer angular acceptance window DX. In most cases normal incidence is used, ai ¼ 0. res ðE; ZÞ is material dependent, Z is the atomic number. The other parameter is the differential elastic reflection coefficient, dre ðE; h; ai ; ZÞ= dX=sr, determined by the scattering angle h. Abundant literature is available on experimental results. The references are given in Table 2. In Table 3 references to dre ðE; hÞ=dX quantitative experimental data are summarized. In the work cited in Table 2, res ðEÞ spectra have been deduced partly from integrating dr ðE; hÞ=dX angular spectra [45,74]. Z ad 2 dr ðE; hÞ es sin h dh ð3:1Þ res ¼ 2p dX ad 1

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Table 2 Measurements of the experimental res ðE; Z; ad Þ data Elements

ad range ()

E range (eV)

Reference

C, Al, Fe, V, Cu, Ag, Ta, W, Au Cu, Ag, Au Cu, Ag, W, Au C, Cu, Mo, Ta Cu Cu, Ag, Au, Si, Ni, Te, Pb Ni, C, Si, Au, Ag, Cu

6–56 5–55 4–44 20–80 5–55 20–70 36.3–48.3

10–2000 150–2000 100–2000 100–2400 100–2000 600–2000 10–5000

[37,38] [93] [94] [45] [95] [74] [65,66,68–71]

Table 3 Meaurements of the experimental dre ðE; hÞ=dX data Element

h range ()

E range (eV)

Reference

Au Al, Ni, Pt C, Cu, Mo, Ta Cu, Ag, Au, Si, Ni, Te, Pb Al, Fe, Ga, Ge, Sb, Tl, Bi

30–150 50–130 100–160 110–160 110–160

100–1000 300–1000 100–2400 600–2000 600–2000

[105] [49] [45] [74] [74]

Integrated reHS ðE; ZÞ elastic reflection coefficients were calculated by Koch, using Monte Carlo analysis based on IMFP data. They are presented in [74] for Si, Cu, Ni, Ag, Te, Au and Pb for E ¼ 0:5–2 keV and are displayed in Fig. 10, for Si, Ni, Te and Pb. Comparison of KochÕs results with Schmidt are given in Fig. 11. In Fig. 12, the res ðEÞ spectra of Ag obtained by different authors are presented. They are compared with some calculated spectra of Ag [106–108] based on experimental data of Schmid et al. [37]. Above 200 eV Jablonski et al. [107] found good agreement with Schmid, as will be discussed in another section. Comparing the experimental reRFA spectra of

Fig. 10. ReHS spectra of some elements [74].

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51

Fig. 11. Comparison of ReHS spectra deduced from experiments of Koch [74] and Schmid et al. [37] denoted by K and S respectively.

Fig. 12. Comparison of experimental reRFA spectra for Ag obtained by different authors [37,74,93,94], and of calculated data [106–108]. Notations are indicated on the figure.

different authors, they exhibit reasonable agreement, except that of Koch, integrated for a lower angular range. The slight differences of Dolinski et al. [93], Golek and Dolinski [94] and Schmid are due to the different angular windows of their RFA, as indicated in Table 2. In Fig. 13, the measured reRFA ðEÞ spectra of graphite [37,45] are compared with JablonskiÕs calculated curve. The agreement is reasonable above E > 300 eV.

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Fig. 13. Comparison of the experimental resRFA spectra of graphite [37,45] with that calculated by Jablonski [107].

3.2. The FWHM, energy distribution, position and intensity of the elastic peak The elastic peak Ie ðEp Þ (and ie resp.) is produced by the sum of elastically backscattered electrons, detected by the spectrometer within its angular acceptance window. In fact, the primary electrons are not monoenergetic due to the energy distribution of the electrons from electron gun. This distribution is determined by the cathode temperature and by the electron optical system of the gun [12,43], resulting in the FWHM DEg . The mean energy of the elastic peak Eme is determined by Ep of the primary electrons. In practice it is nearly identical with Ep , the electrons being scattered without any energy loss. Due to relativistic effects [65,67], the electrons are detected at an energy somewhat below Ep with the electron spectrometer, but this can be neglected for Ep < 3 keV in practice. But there is a physical recoil effect, resulting in energy loss: the Boersch [63,82] shift DEm , produced by Rutherford-type scattering of electrons [13,63,82]. DEm is proportional to Ep and inversely to the mass of the sample atom. The effect is negligible for Ep < 3 keV on high Z elements. This problem will be discussed in Section 4. The exact position of the elastic peak maximum Eme ¼ Ep  DEm . The measured intensity Ie of the elastic peak (and ie elastic current resp.) is affected by the spectrometer. Its shape, FWHM (DEe ) and energy distribution Ie ðEm ; EÞ are determined by DEg , DEs and by the recoil effect [63,82,109]. Recoil broadening DER can be detected with a spectrometer e.g. with DEs < 150 meV [75,83,109]. More details are given in Section 4. Using a spectrometer of good resolution, the principal factor of determining DEe is DEg . The primary electron beam is not monoenergetic. Monoenergetic electrons can be produced by an electron monochromator, used

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e.g. in HREELS and achieving DEg < 10 meV. Such analyzers are available only for E < 100 eV, but operated rather at E < 10 eV. In EPES experiments DEg is typically >100 meV. The ESA 31 is operated at DEg ¼ 150–400 meV. As shown by Schmidt et al. [27] the reRFA ðE; ZÞ experimental spectra obtained with a RFA exhibit characteristic maxima at the energy Ep ¼ Em for solids with Z > 13. For lower Z elements, no experimental data are available. Experimental Em data are summarized in Fig. 14. The values of res ðEm Þ cover the range 3–6.5%. The experimental Em data [27,94,95] can be approximated by a linear relationship with Z [94] as shown in Fig. 14. This was verified by Jablonski et al. [107] with Monte Carlo simulation. They calculated also the reRFA ðEm ; ZÞ values. Their non-relativistic and relativistic data are compared with experimental RFA results in Fig. 15. The agreement is reasonable [107].

Fig. 14. Comparison of experimental Em data [37,77,78,94,110] with JablonskisÕs calculated data [107] for RFA spectrometers. JablonskiÕs notation: (
) non-relativistic, ( ) relativistic calculations.





Fig. 15. Comparison of JablonskiÕs calculated reRFA ðEm Þ data (notations: (
) non-relativistic, ( ) relativistic) with experimental RFA results of Schmid et al. [37], Golek [94], Bideux [77,78], Dolinski [93], and Bondot [95].

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Fig. 16. Experimental reRFA ðEÞ spectra of In (N), Ag ( ) and the calculated spectrum of In (M) [77]. With the courtesy of L. Bideux (University of Clermont-Ferrand).

A special case was found on In, presented in Fig. 16. The broad maximum in the reRFA ðEÞ of In with Em clearly visible in Fig. 16 is interrupted by a sharp minimum around 800 eV [77,78]. Similar anomaly was found on InP [56] and also by Goto on graphite [71]. He attributes it to core level excitation, in disappearance potential spectroscopy (DAPS) [111]. In fact the energy of the In M1 core level is 826 eV, which corresponds to the minimum in Fig. 16. Characteristic maxima and minima occur also in the re ðh; ai ; E; ZÞ spectra. Abundant literature has been published. In Figs. 17–19, four dre ðh; ZÞ=dX experi-

Fig. 17. dre ðhÞ=dX spectra [45] of C, Cu, Mo and Ta for E ¼ 200 eV.

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Fig. 18. dre ðhÞ=dX spectra [74] of Mg, Ge, Te and Pb for E ¼ 1000 eV.

Fig. 19. dre ðhÞ=dX spectra [74] of Mg, Ge, Te and Pb for E ¼ 2000 eV.

mental spectra of Fink [45] and Koch [74] are presented ai ¼ 0. The general tendency of the spectra: the low-energy spectra for E ¼ 200 eV exhibit pronounced maxima and minima, except for C. For higher E, below Z < 30, no maxima are found even at E ¼ 600 eV. Above Z > 30 maxima and minima are found versus h. They are more pronounced with decreasing E and exhibit a monotonic decrease of intensity with E. Figs. 12 and 17–19 refer to absolute values of the elastic peak intensity. A great number of works has been published on the angular variation of the elastic peak intensity in arbitrary units. Some experimental studies are summarized in Table 4. The angular distribution is a material parameter of a clean and smooth surface.

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Table 4 Meausurements of the angular distribution of the elastic peak Element

ai ()

h range ()

E range (keV)

Reference

Au Be, Al, Cu, Ag, Au Be, Al, Cu, Ag, Au Ti, Fe, Ni, Cu, Au Cu Al, Cu, Pt, Au

0, 75 0 75 50, 60 0 0

40–160 90–180 30–150 30–150 120–150 130–165

0.3–2 0.1–2 0.1–2 0.05–0.4 0.2–2 0.2–1

[47] [112] [113] [50] [51] [48]

Like the dre ðE; hÞ=dX results displayed in Figs. 17–19, the AREPES spectra referenced in Table 4 exhibit selective maxima and minima with ai , E and h. They exhibit correlation with the differential elastic-scattering cross sections, to be discussed in Sections 4.5, 4.6, and 5. Many experimental results have been analyzed by Jablonski; he achieved good agreement with experiments using the MC method [48,91,107]. The AREPES spectra are affected by surface morphology, roughness and channeling. 3.3. Morphological effects: diffuse media The surface roughness is an important parameter in EPES. It was measured by SEM [22], STM or AFM by several authors [21,23,28,29]. It is an experimental fact, that res decreases with roughening of the surface [22,37]. The angular distribution dre ðE; hÞ=dX is strongly affected by ion sputtering for scattering angle h > 110 [45]. Oswald et al. [114,115] elaborated a model describing these effects. Kanchenko et al. [116] measured the angular distribution on disordered Al films and on Au [29]. They demonstrated the effect of roughness on elastic scattering. Porous silicon layers (PSL) exhibit a diffuse optical surface. PSL is a diffuse medium for photons and electrons as well. Abundant literature is available on PSL, its preparation, physical and chemical properties, etc. A comprehensive review was presented by Smith and Collins [117]. Samples are prepared by electrolytic procedures [117] on Si crystal substrates. The morphology of PSL is determined by the technology, type and doping of the Si substrate. The porosity P is defined by the volume % of voids. p type (acceptor doped, hole conductor) Si substrate results in sponge type PSL, whereas pþ type Si (heavily doped) produces channel type structure [117]. This review paper is confined to EPES properties of PSL, studied in co-operation with several institutes [30,118–120]. The elastic reflection coefficient res ðE; P Þ of PSL is determined by E, porosity P and strongly affected by its structure (p or pþ Si substrate). A typical reRFA ðE; P Þ spectrum is displayed in Fig. 20, it was obtained on a pþ type PSL sample with P ¼ 78%, as received and treated by HF. HF treatment decreases res , removes the SiO2 surface layer, and produces a stable Si–H bond [30]. A phenomenological model was described in [30,118,120] on the effects of H adatoms. It should be emphasized, H cannot be detected by AES or XPS. EPES proved to be efficient for indirect detection of H adatoms. Their elastic reflection is negligible

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Fig. 20. Experimental reRFA ðEÞ spectra of a PSL (porous Si) sample as received and treated by HF (TH2 ). TH2 refers to the sample etched by HF.

in comparison with Si, O or C (contaminant). In Fig. 21, the calculated elastic reflection coefficients reff of a monolayer of atoms detected by a RFA analyzer are compared for H, Si, O and C [119]. H adatoms attenuate electrons before or after their elastic reflection on the Si surface. For low E electrons (E < 100 eV), the attenuation factor is 20%, as verified experimentally on Si [30,121]. Regarding PSL samples, multiple elastic reflection and attenuation is taking place within the pores, thus decreasing strongly their res [118– 120]. This attenuation is more pronounced for E < 100 eV. In [119,120] detailed experimental results are presented on the effects of P on res ðE; P Þ.

Fig. 21. Calculated reff ðEÞ spectra of a monolayer of Si, O, H and C.

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3.4. Elastic reflection of electrons on single crystal surfaces, diffraction, DEPES, channeling This review paper is mainly dealing with incoherent elastic scattering of electrons by solid surfaces. Coherent elastic scattering takes place in diffraction. LEED is beyond the scope of this paper. Hereupon only a brief outline is given on some special cases. Medium energy electrons exhibit Kikuchi patterns [122]. McDavid and Fain [44] studied the elastic peak intensity versus E with a CMA on an Ag(1 1 1) crystal. They observed selective maxima of Ie ðEp Þ and identified them with calculations diffraction at the 42 CMA angle. Their procedure was applied to check amorphized surface layers and crystallinity of the sample after ion bombardment [16]. Mroz et al. [123–125] developed directional EPES (DEPES). They worked with a RFA averaging the Ie ðEp ; hÞ signals and studied them versus the angle of incidence of primary electrons. They found selective maxima with ai , when the electron beam was parallel to close packed atomic rows, enhancing elastic scattering in the forward direction. The ai dependence of the Auger signal was similar to DEPES spectra [123,124]. The positions of the maxima were not dependent on E. Mroz et al. presented a phenomenological model explaining their experimental results for Cu [124] and for Ag layers deposited on Cu(1 1 1) [123]. DEPES proved to be an efficient tool to study roughening of Cu at elevated temperature [125]. Imperfect amorphization of III–V crystals produces DEPES or channeling effects, as shown in Fig. 22. The Renninger plot of InSb exhibits fluctuations in the intensity Ie ðEp ; /Þ plotted versus the azimuthal angle /. The sample was rotated around the axis normal to its surface. The crystallinity of the sample can be characterized by the contrast factor Cf [125] in the Renninger plot. Cf ¼ ðhmax  hmin Þ=ðhmax þ hmin Þ, hmax ¼ maximum in elastic peak intensity, hmin ¼ minimum. In practice, Cf should be <0.1. Incoherent elastic scattering occurs in the position of / producing the hmin in the Renninger plot [16].

Fig. 22. Renninger plot obtained on amorphized InSb(1 0 0) surface layer, Ep ¼ 2 keV.

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Channeling also enhances the intensity of the Auger and elastic peaks. These effects occur in SAM when studying crystals with grain boundaries and varying the angle of incidence of the electron beam. Doern et al. [126] developed a procedure for correcting the Auger peak intensity with the Ie ðEp Þ for polycrystalline Cu. Channeling and DEPES effects appear in Kikuchi patterns [127]. They are characterized by Renninger plots [16,127]. Channeling effects can be detected also by tilting the sample.

3.5. Temperature effects in EPES Except for low-energy electrons (E < 200 eV), elastic scattering is a phenomenon of atomic physics (see Section 4), determined by the elastic-scattering cross sections of the individual atoms. Temperature effects have been studied in early works [128– 131], where the angular dependence of elastic scattering on atoms with solid or liquid targets was studied. The generally poor vacuum available at the time produced artifacts [128–130]. Schilling and Webb [131] studied Hg in liquid and vapour phase in the E ¼ 100–500 eV range in UHV. They observed attenuation in the liquid due to inelastic scattering of electrons. Another type of temperature effect was described by Mroz and Mroz [125], who studied the temperature effect with DEPES and DAES for Cu(0 1 1) in the T ¼ 500–1100 K temperature range. He defined the contrast factor Cf, based on the ratio of maximum and minimum intensity of the elastic peak Ie ðEp ; ai Þ. The Arrhenius plots of the CfðT Þ factor exhibited characteristic sections determined by the Debye–Waller effect, by anharmonic vibrations, and above T > 1000 K by the roughening of the sample. The recoil effect is sensitive the temperature of the surface. Boersch et al. observed temperature broadening of the elastic peak [82].

3.6. Extended fine structure of elastic scattering, EXFSEPES Conventional, widely applied methods for the study of atomic interactions with near neighbor atoms are EXAFS (X-rays) and EXFSEELS (REELS) [132]. The elastic peak Ie ðEp Þ exhibits similar fine structure as in the X-ray absorption or in the REELS loss spectrum. In [13] a brief review was given on EXFSEPES. Lin and Khan [133,134] and Bondarchuk et al. [135] elaborated the procedures. The extended fine structure of Ie ðEp Þ was measured with a RFA operated in the derivative mode. They used also a LEED system completed with three small size analyzers of Dh ¼ 3 collection angle. They made the experiments at three different H scattering angles and scanned Ep [135]. The Ie ðEp Þ spectrum was subjected to smoothing, background subtraction and Fourier transformation. Lin and Khan [133,134] and Bondarchuk et al. [135] developed theoretical models for the interpretation of the experimental results. Their work resulted in the determination of interatomic distances in Si and amorphized aSi–O, Si–C [133], Ge, aGe, GaP [135]. They found excellent agreement with literature data. Amorphization was produced by Arþ ion bombardment.

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3.7. Spin polarized elastic scattering, SPEPES Experimental research of spin polarized (SP) electrons goes back to the sixties. The early works [128–130] were dealing with AREPES of electrons on atoms using Mott detectors operated at high voltage (E > 100 keV). SPLEED opened a new field of research. An excellent review was given on SP electron spectroscopies in the book of Kirschner [136] and in the recent monograph of Hopster [15], which contains also a comprehensive list of the rich literature. Nowadays a laser pumped GaAs source is used to produce a beam of spin polarized electrons. Low energy (100 eV) LEED detectors developed by Kirschner, consisting of a W(1 0 0) crystal or poly Au film can be used to measure the spin polarization of the scattered electrons. In practice, SPEPES is based on SPLEED. It proved to be advantageous for the study of very thin magnetic films and layer structures [15,137]. An advantage of SPEPES is its very low information depth (some ML of atoms). An interesting feature is the different IMFP of up and down spin electrons, as described in another paper by Hopster [137,138].

4. Physical processes in elastic backscattering of electrons 4.1. Electron impact and SEE Elastic backscattering of electrons manifests itself by the elastic peak. Elastic backscattering is produced by several elementary processes, determining the trajectory of electrons. In Table 5, a survey is given of the elementary processes and the corresponding physical parameters. In the following, these processes will be briefly discussed. Primary electrons hitting the surface penetrate into the solid, and their energy Ep is conserved until the first inelastic collision. The mean escape depth of elastically reflected electrons is determined by ke and IMFP ki . Quantitative EPES requires knowledge of ip , the primary current. Ideally it should be measured with a Faraday cage, as in GotoÕs CMA the Faraday cage is incorporated in the sample holder [41]. In most cases however a Faraday cage is not many available in electron spectrometer systems. ip can then be estimated from the sample current is , detected with a biased sample holder. Many spectrometers are provided with visualisation facilities of the sample and for selecting the spot to be analyzed. A conventional method uses a wire loop collecting the secondary ise (SEE) and backscattered irb (elastic and inelastic) electron current. From KirchoffÕs law, ip ¼ is þ ise þ irb

ð4:1Þ

is and irb can be measured by biasing the collector loop and the sample. The backscattering coefficient rb ¼ irb =ip was determined by Cazaux et al. [139]. The coefficient of secondary electron emission rse ¼ ise =ip is obtained by convention from electrons of E < 50 eV energy. It can be determined by biasing the sample with a positive voltage of 50 eV. rb is a material parameter [53]. Reliable formulae are

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Table 5 Elementary processes of elastic backscattering Process

Parameter

Observable by experiment

Electron impact Penetration into the surface Electron backscattering

Ep , ip , ai

Sample current is SEE irs irb

Electron refraction Recoil effect Surface excitation Very low energy losses

ai , a0i , Vi Ep , Z, Epls , Ps ðEÞ, ai DEs , Ep , Eph

AREPES Ep < 100 eV EPES Em position, DER EELS, IðEpls Þ EL < DEg , LEEELS

Elastic scattering Recoil effect Single elastic scattering

ke , drðE; h; ZÞ=dX DER , Ep , M h, ad analyzer

Double elastic scattering Recoil effect Multiple elastic scattering Escape of electron Refraction before escape Surface excitation

ke ðEÞ Poissonian DER , Ep , M E ¼ Ep , ad analyzer ad , a0d analyzer Ps ðEÞ, ad

EPES EPES EPES, predominant for Ep < 100 eV EPES, Ep EPES EPES, ie ðEÞ, DEe EPES, IMFP ki AREPES Ep < 100 eV EELS, IðEpls Þ

Inelastic scattering and escape of electron

IMFP ki ðEÞ, Epl1 plasmon energy

EPES–EELS

available for calculating rb . August and Wernisch [96] give a critical review of the previous literature and formulae for rb ðE; ZÞ. 4.2. Refraction of electrons Primary electrons penetrating into the solid are refracted [13,140], as shown in Fig. 23. ai is changed to a0i the angle of refraction [140]. The refraction is described by [13,116,140].

Fig. 23. Refraction of electrons penetrating into the solid and escaping. The angles of refraction are indicated.

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sin ai = sin a0i

sffiffiffiffiffiffiffiffiffiffiffiffi 1 þ Vi ¼ Ep

ð4:2Þ

In Eq. (4.2) the determining parameter is the Vi internal potential of the solid. Vi was determined experimentally from the angular distribution res ðE; hÞ of elastic scattering and resulted in Vi ¼ 14  1 eV for Au [140]. This is a typical order of magnitude. According to Eq. (4.2), the refraction might be observed at low Ep energies, in practice <100 eV. 4.3. Very low energy loss processes Primary electrons penetrating into the solid suffer elastic or rather quasi-elastic scattering by the atoms. Low-energy losses are produced by the recoil effect, by phonon or intraband losses and by surface excitations. They are integrated by the energy window and DEs of the spectrometer. Rutherford-type scattering results in the recoil effect in electron–atom collisions, producing a loss DEm on a free atom [63,82]: DEm ¼ 4ðm=MÞE sin2 ðh=2Þ

ð4:3Þ

where m is the mass of the electron, and M is the mass of the atom, a function of Z. According to Eq. (4.3), DEm increases with E, h and 1=Z. In a solid, the energy loss DEm is transferred to the crystal lattice. The effect has been described by Boersch et al. [82]. They studied a number of elements covering the range Z ¼ 4–79, M ¼ 9–195, h ¼ 45–135 and Ep ¼ 20–40 keV. The graphite sample was measured at T ¼ 150 and 1600 K and exhibited broadening of DER with temperature [82]. Makarov [13,141] compared the elastic peak position of C, Al and Pt at Ep ¼ 14 keV and used EPES for surface analysis. Laser and Seah [63] published systematic studies on Cu, Ag and Au for Ep ¼ 200–3000 eV, and determined shift of the position of the elastic peak with Ep . They and recently Goto [65] proved experimentally the formula of Boersch. Our very recent experiments with the ESA 31 spectrometer on graphite, Si, Ni, Ag, Au and LiF, using high resolution (DEs ¼ 55–132 meV) confirmed also Eq. (4.3) for E ¼ 1–5 keV [109]. The broadening of the elastic peak (FWHM) DER was studied in detail in [141–143]. The recoil broadening of Si at E ¼ 5 keV resulted in DER ¼ 130 meV but it was negligible for Au. The broadening was considerable for graphite. Boersch et al. [82] attributed the recoil broadening to the Doppler effect. The incident electron hits vibrating with its thermal energy. The Doppler effect pffiffiffiffi the atom pffiffiffiffi ffi would produce a E and 1= M relationship for the broadening. This was verified experimentally, but the broadening for Si and graphite proved to be larger than expected from the Doppler effect [109,142,143]. The recoil broadening is considerable for low Z elements and compounds [109]. DEm and DER are produced by the sum of subpeaks for the constituents of the compounds, each producing a recoil shift and broadening [109]. The total intensity is determined by the relative intensities for the constituents which are a function of the elastic-scattering cross sections; the latter

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increase with Z. For a compound containing low and higher Z elements, intensities for the latter should dominate the elastic peak [109]. Laser and Seah [63] attributed the recoil broadening to multiple elastic scattering, this, however, is almost negligible for low Z elements [143] and cannot explain the large broadening for graphite. An important factor might be phonon losses: for Si, Eph ¼ 56 meV [144]. For GaAs, Eph ¼ 23:5 meV [145], and other III–V compounds exhibit similar values. It is hardly possible to separate them from DER . No phonon losses were observed on a clean Ni surface [101]. On the other hand, Eph ¼ 200 meV was found for graphite [146] and similar value for Al2 O3 [147].

4.4. Surface excitation Surface plasmons are a particular type of surface excitation, given by the imaginary part of the dielectric function Imf1=ð1 þ eÞg. The book of Raether [148] devoted a big chapter to surface excitations and to surface plasmons. Incident electrons produce surface excitations and surface plasmons within the first few monolayers of the selfedge [11]. They appear in the REELS spectra. In plasmondominated loss spectra, surface plasmon loss peaks are present in the E ¼ 1–20 eV range. Surface plasmons are observed predominantly in semiconductors and some metals [148], but, in general surface excitations occur in solids. Surface plasmons can be excited by electrons in the vacuum approaching the surface or leaving the surface [11]. The probability of excitation of surface plasmons is decreasing with E, however even 5 keV electrons produce them [6]. They are strongly dependent on the angular conditions [4]. Surface plasmons are characterized by the SEP Ps . Ps denotes the average number of surface plasmons produced by an electron crossing the surface once [4,11]. In EPES, both the incident and escaping electrons can excite surface plasmons. The SEP parameter for EPES will be denoted by Pse . Recent experimental data on Pse are presented in Section 6.4. Surface excitation is a competitive process to elastic scattering, decreasing re with respect to its calculated value based on bulk parameters. A very rich literature is available on surface excitation. Here only some fundamental works are mentioned [4,11,148–152], summarizing the available literature. Recently, surface excitation became the focus of interest. Pse was calculated with the model of Oswald [114] by [4] presenting a simple relationship: Pse ðEÞ ¼

1 1 pffiffiffiffi þ pffiffiffiffi as E cos ai þ 1 as E cos ad þ 1

ð4:4Þ

where as is a material parameter. Its values are typically between ð0:7–1:0Þ  0:173 eV0:5 and summarized in [4,153] for some free electron like materials. The experimental determination of Pse will be discussed in Section 6.4. Using a CMA, the low-energy losses due to surface excitations in Cu [17] and GaAs produced asymmetrical broadening of the elastic peak, while it was symmetric for Si and Ni.

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4.5. Elastic scattering of electrons: differential elastic-scattering cross sections The elastic peak intensity and re as well are determined predominantly by elastic- and inelastic-scattering processes, characterized by the elastic-scattering cross sections and by the elastic and inelastic mean free paths of electrons, ke and ki respectively. The incident electron interacts with an atom. The interaction might be elastic or inelastic. The elastic peak is formed by electrons suffering single, double or multiple elastic-scattering events, a scheme is presented in the Fig. 24. Such a picture also describes multiple-scattering theory of LEED. Elastic scattering is a long range and most intense electron–atom interaction [12]. It is characterized by its cross section. The differential elastic-scattering cross section drðE; Z; hÞ=dX is determined by E, Z and h. The total elastic-scattering cross section rT is [154]: Z p dr sin h dh ð4:5Þ rT ¼ 2p 0 dh where again h is the polar scattering angle. drðE; Z; hÞ=dX and rT are fundamental quantities characteristic of the atoms of a material. A very rich literature has been published on drðE; Z; hÞ=dX. Some important data and results will be cited below. Elastic scattering for EPES is in contrast to LEED is mainly an atomic-collision process. This is valid for an amorphous or disordered solid. Coherent elastic scattering, diffraction of electrons occurs on ordered, crystalline structures.

Fig. 24. Scheme of electron trajectories suffering single, double and triple elastic scattering.

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Fig. 25. Comparison of the differential elastic-scattering cross sections on free and bound Cu atoms [155].

drðE; Z; hÞ=dX is determined by E, h, Z and by the electron atom-potential. Solid state effects occur at low energies, in practice for E < 200 eV [155,156]. In Fig. 25, drðEÞ=dX are compared on Cu for free and bound atoms, i.e. solid Cu. The latter shows systematically lower values with respect to the free atoms at E ¼ 200 eV, but the difference is negligible at 1 keV. The simplest approach for the elastic-scattering event can be given by the Rutherford scattering equation supplying the Rutherford cross section: dr=dX ¼ 4:97  1021

Z2   ðcm2 sr1 Þ E2 sin4 h2

ð4:6Þ

E is expressed in keV [157,158]. Exact calculations of dr=dX use quantum mechanical methods. After the pioneer works of Bauer and Browne [159], Fink et al. [160–162] and Riley and MacCallum [163] published tabulated data for a great number of elements and covering wide energy ranges. Ichimura et al. [164] calculated Mott cross sections and they introduced the Mott factor RM , drðE; Z; hÞ=dX ¼ RM dr=dX defined by Eq. (4.6). Reimer and Loedding [158] calculated the Mott cross sections by solving the relativistic Dirac equation. Mott factors have been published also in [165]. Nakhodkin and Melnik [13] reviewed some other relevant papers. Joy et al. [166] supplies calculated drðE; Z; hÞ=dX data on disk. The NIST supplies a

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Fig. 26. Comparison of drðhÞ=dX on Cu for E ¼ 100 eV. Notations: full line [160], broken line [9]. Reproduced with the courtesy of C.J. Powell (NIST).

database of elastic-scattering cross sections [9] calculated by Jablonski [167] using the partial wave expansion method (PWEM). In our present works we are using this NIST database. In fact, cross sections of the NIST database are in reasonable agreement with the published data except [160–162], where a systematic factor of about 4 appears to be due to the mistake in units in the latter works. In Fig. 26, the drðhÞ=dX values from the NIST database are compared with those from [160] for Cu at E ¼ 100 eV. Salvat and Mayol [168] described a computer method for calculating the cross sections. In the following a brief outline is given on the calculation of drðE; hÞ=dX, described by Jablonski [167,169]. The interaction between an electron and the central field potential Vi ðrÞ is described by the Schroedinger equation. At large distances from the atom the solution is approached by the superposition of the plane incident wave and the outgoing spherical wave. The dependence of interaction on the scattering angle h angle is given by the amplitude f ðhÞ associated with the differential elastic-scattering cross section. drðhÞ=dX  f 2 ðhÞ. Jablonski used the PWEM method, expanding the wave function in a series of Legendre polynomials, since the scattering is axially symmetrical with respect to the direction of the incident electron. Riley and MacCallum [163] used Laguerre polynomials. Jablonski [169] applied the Thomas–Fermi–Dirac (TFD) potential. He developed also a relativistic approach [167]. The atomic potential Via dependence of dr=dX is strongly affected by the type of Via at low energies (E < 50 eV) [170,171]. In a very recent work, Jablonski and Powell [172] compared the effects of various atomic potentials on the differential and total elastic-scattering cross sections, etc. They studied the TDF, the DHFS (Dirac– Hartree–Fock–Slater) and DHF (Dirac–Hartree–Fock) potentials for six elements and the 100 eV–10 keV energy range. They found considerable differences (a factor of 2) for low scattering angles (H < 10). The total scattering-cross sections rT resulted in similar differences for E < 1000 eV using different atomic potentials.

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Finally, rT should be mentioned. The elastic mean free path ke is determined by rT . Many data have been published in tables and figures in references [9,158, 159,163,165,172,173]. 4.6. Single and multiple elastic scattering of electrons: ke and ki IMFP An incident electron reaching an atom can suffer elastic or inelastic scattering. The probability of elastic scattering is generally much higher than that for an inelasticscattering event. The mean distance between two elastic collisions is the elastic mean free path ke , defined by Bauer [154]. ke ¼ 1=rT NA , where NA is the density of atoms/ cm3 . The probability of elastic scattering obeys a Poissonian distribution [167]. Several (1, 2, etc.) subsequent elastic collisions can take place. The electron conserves its energy until the first inelastic-scattering event. The mean distance between two inelastic scattering is the IMFP ki , defined by an ASTM standard [174]. In the pioneer period of AES, XPS and surface science, the concept of ki was not assessed and it was confused with kAL , the attenuation length of the electrons. Nowadays ki ; kID (information depth), kED (escape depth), etc. are defined by ASTM and ISO standards. It should be underlined, ki is a physical material parameter, suitable for calculating other parameters kID , kED ). The IMFP will be discussed in Section 6.2. The early work of Seah and Dench [175] presents kAL data. In a recent monograph and very recent paper Powell and Jablonski [7] published a comprehensive review on the IMFP, its calculation and a critical treatise of experimental results in the literature on elements and some compounds. In this section a brief review is given of literature on the calculation of ki . Tanuma et al. [103] elaborated on a procedure based on the dielectric function, actually its imaginary part. The imaginary part of Imð1=eÞ gives the probability for inelastic scattering of electrons. The dielectric function can be deduced from the total optical reflection spectrum, determined by synchrotron spectroscopy. The IMFP is inversely proportional to the total cross section for inelastic scattering (i.e. for inelastic processes involving excitations of both valence and core electrons). Tanuma et al. [103] summarized calculated ki data on 27 elements and 15 inorganic compounds, later on organic compounds [176]. They cover the energy range E ¼ 50–2000 eV. Nowadays quantitative surface analysis uses TanumaÕs data. They have been confirmed by experimental results for metals [99,100] on Si and Ge semiconductors [177] and III–V compounds [178–181]. Werner et al. [182] determined ki for 24 elements, and these results agreed with Tanuma et al. calculations. Besides the NIST [183] data, ki was calculated by Ashley and Tung [104] for E ¼ 0:4–10 keV. In the overlapping energy range his data are in reasonable agreement with Tanuma [103]. Kwei and Chen [184] calculated ki on III–V compounds for E ¼ 0:2–10 keV. Gries published a predictive formula for ki [185,186] based on the Tanuma data.. Nefedov et al. [187] developed an approach based on the Hartree– Fock approximation for calculating ki . In many cases [104] the approximative equation was used: ki ¼ aEp

ð4:7Þ

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where a and p are material parameters, valid for selected energy ranges [104]. Jablonski [188] deduced a universal formula, based on BetheÕs loss function: ki ¼ aE= lnðcEÞ

ð4:8Þ

where a and c are material parameters. They are determined by experiments [179,180]. As shown in Tougaard Õs approximative formula [189]: Z Ep 1=ki ¼ KðEp ; EL Þ dE ð4:9Þ 0

K is the probability of energy loss EL per unit path in the solid. K is the inelasticscattering cross section. Quantitative surface analysis uses the attenuation length kAL , particularly for the measurement of overlayer film thickness. It was calculated by Cumpson and Seah, comparing kAL with TanumaÕs ki data [190]. The trajectory of an elastic electron in a solid in EPES is mainly determined by elastic-scattering events. Angular deflections are results of inelastic scattering and can be generally ignored. The trajectory terminates with the escape to the vacuum (elastic backscattering) or by an inelastic-scattering event. The flux of electrons is attenuated by inelastic scattering [107,167]. The electron trajectories can be simulated. The spectrometer detects the elastic backscattered electrons only. The calculated IMFP values refer to inelastic scattering in the bulk of the solid. Low-energy E < 200 eV electrons are reflected elastically from shallow depth, typically 1–2 monolayers (ML). EELS experiments on very thin films revealed, that they exhibit bulk behaviour for thickness greater than 3–4 ML. 1–2 ML thin films are two dimensional systems [191]. In their loss spectra, surface plasmons dominate. The same is valid for REELS spectra at low Ep energies. Our experiments on GaSb [180] showed the marked contribution of surface plasmons (Fig. 27). At low energies (E < 200 eV) surface excitation plays a dominant role in the IMFP. Chen and Kwei [192] introduced the depth dependent IMFP. In addition, the IMFP can be spin dependent. Abraham and Hopster [137] verified experimentally its spin dependence in ferromagnetics. He gave quantitative interpretation of experiments for 4 ML Fe

Fig. 27. Comparison of REELS spectra of GaSb, measured at E ¼ 0:2 and 2 keV.

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on Cu(1 0 0) at 100 K. Section 6.2 will be devoted to experimental determination of the IMFP. 4.7. Life time of hot and medium energy electrons The IMFP is determined by the product of the velocity v and lifetime s of the electron [8]. (We assume that the kinetic energy exceeds the thermal energy). Recently the problem was discussed in a review paper of Echenique et al. [8] for E < 5 eV. Time-resolved two-photon photoemission spectroscopy (TR-2PPE) supplied experimental s data for a number of metals [8,193] and the experiments yielded good agreement with calculations [8,194]. The method however is confined to hot electrons with E < Ew (Ew work function) of the metal. EPES deals with medium energy electrons of E ¼ 100 eV–5 keV. For E > 5 keV relativistic effects occur. The velocity of free electrons in the non-relativistic limit is given by rffiffiffiffiffiffi 2E v¼ ð4:10Þ m Assuming a power law for the IMFP ki E0:8 , the electron life time should show a dependence s E0:3 , s was estimated from the IMFP values of Tanuma et al. [103] and resulted in 2 fs for Cu at E ¼ 1 keV. Below E < 50 eV, s can be estimated only by extrapolating data in [8]. The measurement of s in solids above E > Ew is a task for the future.

Fig. 28. The percentage of contribution of one, two, etc. elastic scattering events in re , plotted versus E and obtained by MC simulation for Cu [195].

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4.8. Escape of the electron from a solid surface Before escaping, an electron can produce surface excitations and will suffer refraction, as shown in Fig. 23. Except at very low E (E < 50 eV), refraction can be neglected. Electrons of E > Ew will escape. The escape of medium energy electrons is dominantly determined by backscattering processes, i.e. the elastic and inelasticscattering cross sections. Depending on E, the relative contribution of electrons suffering single, double etc elastic-scattering events is displayed for Cu [195] in Fig. 28. The elastic peak is composed of reflected electrons detected within the spectrometer angular window. The calculation of electron trajectories will be discussed briefly in Section 5. 5. Calculation of elastic reflection of electrons The main processes are discussed in review papers [1,2,4]. The first papers on EPES [12] used a single elastic-scattering approach. Reliable interpretation of elastic backscattering of electrons needs calculation of electron trajectories, as determined by elastic and inelastic scattering processes. Since l981, three types of approaches have been developed: the layer model with single scattering, Monte Carlo (MC) simulation, and an electron transport algorithm. The goal is the interpretation of experimental results such as: • res ðE; Z; ai ; ad ; DXÞ; • re ðE; Z; h; ai Þ angular dependence or distribution per sr; • Ies ðEÞ=Ier ðEÞ the ratio of the elastic peak intensities measured on the sample with a reference standard. In the following a brief review will be given on the methods and results. 5.1. The layer model with single-scattering approach Gruzza and Pariset [196] calculated the elastic reflection of electrons on ordered atomic layers, measured with a RFA. The model is valid also for subsequent alternating atomic layers, measured on III–V crystals. Their surfaces were modified by Arþ bombardment cleaning and heat treatment [32]. The single scattering approach proved to be useful for low E (E < 500 eV) electrons for the study of InP(1 0 0). The re ðEÞ experimental spectra were compared with the calculations simulating various atomic arrangements and resulted in interpretation of experimental data [32]. The surface enrichment of In by Arþ sputtering has been described. 5.2. Monte Carlo (MC) simulation in EPES Monte Carlo simulation of elastic backscattering is discussed in detail in review papers [1,2,4]. It has been described by Jablonski et al. in a great number of papers

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cited in this review paper. This is also a classical problem of SEM and SAM [197,198]. The MC simulation proved to be a powerful tool for all EPES problems. This section is confined to EPES problems and applications. The MC simulation supplies the elastic reflection coefficient res ðE; Z; ai ; ad Þ for any type of electron spectrometer or for re ðE; Z; hÞ, and the angular distribution of elastic reflection. Recently, software was developed by Jablonski et al. for any type of spectrometer, angular conditions and reference sample [199]. The MC analysis needs knowledge of drðE; hÞ=dX and assumed values of ki ðEÞ for the material studied. The MC algorithm was developed for a perfectly smooth surface and a disordered distribution (amorphous) of atoms. It is not valid for ordered crystals resulting in coherent elastic reflection: Bragg diffraction, channeling [16], or DEPES [123]. Several methods of MC have been published. In the following a brief description will be given, based on JablonskiÕs works [107,167]. A similar description was also published in. [195]. An MC simulation for a Au/Si layer structure was described by Kwei et al. [200]. The MC algorithm calculates the trajectories of typically 106 –107 electrons. The trajectories are described by a Poissonian stochastic process. Using a linear elastic step length s, the probability density function P ðsÞ is   1 s s P ðsÞ ds ¼ exp  exp  ð5:1Þ ke ke ki An inelastic-scattering event can take place, characterized by the IMFP along the trajectory. This probability appears in the second factor in Eq. (5.1). The elasticscattering process can be described by the probability density function: P ðhÞ ¼ 2p sinðhÞðdrðE; hÞ=dXÞ=rT

ð5:2Þ

where rT is the total elastic-scattering cross section. The contribution of the kth trajectory in the elastic current is Dik . The elastically scattered electrons detected by the spectrometer are those found within its angular window and integrated by following n electron trajectories. They are summed res ðE; DXÞ ¼

n 1X Dik n k¼1

ð5:3Þ

The calculation of trajectories is continued until res becomes constant. Jablonski found reasonable precision with a total number of trajectories >106 [107]. His algorithm was elaborated for binary III–V compounds [167,178,179] even with a surface composition different from the bulk. The validity of JablonskiÕs method was confirmed by its good agreement with many experiments. In a recent work Jablonski et al. analyzed the effects of the interaction potential on MC simulation of the DDF on Be, C, Al, Cu, Ag and Au [172]. Other authors developed different MC simulation methods. Robert et al. [201] developed an MC algorithm for layer structures of III–V crystals using BondotÕs method [93,95]. They calculated the fraction of escaping electrons from the first,

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Fig. 29. Percentage of electrons collected by a RFA, escaping from the first, second, etc. ML on a Cu surface [95].

second, etc. atomic layers of Ni, Ag and Au [202], as illustrated in Fig. 29 for Cu [95]. These calculations involve also the depth distribution function of elastically backscattered electrons and the information depth of EPES. Bondot introduced the Schroedinger equation and its solution with Legendre polynomials into his computer program. The special feature in this work is that the calculation of the trajectory is terminated when arriving at a path length of ki . Fitting et al. [203] starts calculations with the dielectric function and core level excitations, thus calculating ki also with his program. Toekesi incorporates into his program the calculation of scattering cross sections and with the use of the dielectric function he obtains ki [98]. He obtained similar ki values as those found by Tanuma et al. He calculated reCMA ðE; ZÞ for a number of elements and found good agreement with the results of Koch [74,75]. MC simulation was used for interpretation of re ðE; Z; hÞ AREPES spectra on Au [204,205], and on Ag [206]. Ding et al. [207] published MC simulation for EPES working with a CMA. 5.3. Analytical solution of the electron transport equation This section is devoted to electrons reflected from a solid surface, as discussed in detail in [1,4]. Recently, Dubus et al. [2] summarized the problems in a monograph. In the following a brief review is given on some important works. It was started by Tougaard and Sigmund [208], who analyzed the transport problem in solids. Dwyer [209] was the first to solve the backscattering problem with the Boltzmann transport equation very approximately. Tofterup [210] used the P1 approximation to solve the transport equation and he obtained very approximate results. Later Tilinin and Werner [211,212] published a very extended solution of the transport equation. The problem goes back to reactor physics [209]. Werner et al. [49] achieved equivalent results with MC simulation and good agreement with AREPES experiments on graphite, Al, Ta, Pt and Au for E ¼ 0:2–2 keV and h ¼ 40–180.

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Tombuyses et al. [213] created an analytical model for elastic backscattering. Sjoestrand [214] numerically solved the transport equation for AREPES on Al, Cu and Au, achieving good agreement with the MC method. Borodyansky and Tougaard [215] calculated the path length distribution function for backscattered electrons, using a very simplified model. Oswald et al. [114,115] presented a theory on electron reflection and its angular distribution for single, double and multiple elastic-electron-scattering. They found good agreement with experiments for C, Cu, and Ta, and gave an interpretation of FinkÕs experimental results [45]. They found good agreement with MC simulations. The analytical solution consists of complex mathematical formulae. The transport mean free path is an important parameter used in the calculations [3,172,211, 212,216]. Very recently, Jablonski [216] compared the MC simulation with the transport method. In another recent work he analyzed the effects of interaction potential working with the transport method [172]. A special application of the transport model was the elastic backscattering for the Au/Ni layer structure [217].

6. Determination of physical and material parameters by EPES EPES proved to be an efficient tool for experimental determination of physical and material parameters needed by quantitative surface and thin film analysis. The parameters needed for analysis of the experimental results are: • • • • • • •

drðE; ZÞ=dX (differential elastic-scattering cross sections); ki (IMFP of the electrons); KðE; EL ; ZÞki ðEÞ (inelastic-scattering cross sections); Pse ðEÞ (surface excitation parameter); ri ðE; ZÞ (inner shell ionization cross sections); rsv (cross sections for excitation of surface vibrations in adatoms); rEID (cross sections for electron induced desorption). In the following a brief review will be given.

6.1. The differential elastic-scattering cross sections drðE; Z; hÞ=dX of electrons The experimental determination of drðE; Z; hÞ=dX can be based on combining res ðE; Z; h; ai Þ%=sr and drðE; hÞ=dX angular spectra. Bibliographical sources are summarized in Tables 2–4. The MC simulations are discussed in [1,4]. The spectra supply dr=dX, provided, that the accurate ki data are available. Jablonski [48,107,167], Oswald [114,115] and Kochur [206] interpreted AREPES spectra, using MC simulation or the transport method. MC was based on dr=dX and ki data. Their reasonable agreement with experiments proves the validity of MC and transport methods, and also for the ki data used and of the calculated dr=dX data. I am not aware of any determination of dr=dX by evaluation of experimental results, except the works of Kanchenko et al. [13,116,218]. They showed, that for

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E < 100 eV the majority of electrons suffer single scattering, whereas multiple elastic scattering occurs for larger energies. They determined drðEÞ=dX for Au with E ¼ 100–2000 eV [116]. Experimental determination of dr=dX was performed in low-pressure gases; this work however, is beyond the scope of this paper. Some results are presented for H by Williams [219], for rare gases in [220,221] and for vapour and liquid Hg by Schilling [131]. 6.2. Experimental determination of IMFP ki Powell and Jablonski present a comprehensive review in their monograph [7] on calculation methods and experimental results available in the literature. The IMFP data available are summarized in the NIST database [183]. This section is confined to the EPES method. It is based on the measurement of the elastic peak intensity [12,222]. There are three kinds of experiments: • The measurement of re ðE; Z; ai ; ad Þ using a RFA analyzer [37,76–79]. • The measurement of re ðE; Z; h; ad Þ=sr, AREPES with a rotable analyzer [45,49,74]. • Measurement of the integrated intensity ratio of elastic peak Ies ðEÞ=Ier ðEÞ sample with a reference standard sample [223]. All of these experiments are evaluated by MC simulation procedures. The reRFA ðE; ZÞ MC algorithm was developed by Gruzza et al. [93,95]. Working with k as free parameter and fitting the calculated data to experiments supplied the experimental ki data [7,183,222,223]. A similar method was used by Oswald [114,115], who applied his procedure to the experiments of Fink [45], as shown in Table 2. Koch succeeded in the experimental determination of IMFPs for a number of elements, as shown in Table 2, from evaluations of AREPES experiments. The reference method was started with an Al reference standard [223]. Later Ni proved to be better [99,100]. More recently Ag proved to be similar to Ni [181,224], but less sensitive to contamination by residual gases (CO). According to [17] Cu is not favourable for the CMA, due to its loss spectrum. The MC simulation with k as a free parameter supplies working curves for each energy E. For the ki of the reference sample (Al, Ni), TanumaÕs data were used. Experimental data are fitted to the working curves, and thus supply experimental values of the IMFP. The procedure is illustrated in the Fig. 30, which shows some working curves for Si/Ni to be used in the analysis of experimental measurement of IeSi =IeNi as indicated for each energy. The IMFPs are on the abscissa on this figure. JablonskiÕs MC algorithm described in Section 5.2 is used in our present work and makes use of drðE; hÞ=dX data from the NIST [9] database. In practice the ki values for Ni from TanumaÕs and from AshleyÕs results [104] are similar, thus above E > 2 keV the latter can be used. A problem was met with single crystals. The MC algorithm is based on an assumed disordered surface layer. Such layer was produced by amorphizing the surface layers with Arþ ion bombardment [16]. The more serious problem might be insufficient amorphization. Orientation effects in the elastic peak

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Fig. 30. Calculated working curves for evaluating experimental EPES data obtained with the ESA 31 spectrometer on Si with Ni reference. k is plotted on the abscissa. T denotes TanumaÕs data.

can increase its intensity. Such effect can be revealed by rotating the sample around the axis perpendicular to its surface [16]. The variation of Ie ð/Þ with azimuthal angle / is measured in Renninger plots. A Renninger plot for InSb is presented in Fig. 24. Greater difficulty was met for the case of III–V compounds, since prolonged highenergy ion bombardment produces decomposition of the crystal and segregation of one elemental species on its surface. These effects are illustrated in Fig. 31, which shows strong distortion of the loss spectrum and the growth of a EL ¼ 13:7 eV loss peak in the REELS spectrum of GaSb [180] bombarded by 10 keV Arþ ions. This result proves the surface segregation of Ga. The incoherent scattering intensity of the elastic peak, obtained at the minimum of the Renninger plot [16], was utilized to determine IMFPs. The MC algorithm of Jablonski was applied taking into

Fig. 31. Comparison of the REELS spectra of GaSb subjected to 2 and 10 keV Arþ ion bombardment. The elastic peaks are fitted at Ep ¼ 2 keV.

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consideration the surface composition [179] measured by XPS. The validity of this procedure was confirmed by the reasonable agreement of our experimental IMFPs with those calculated by Tanuma [103] and Kwei [184]. The procedures outlined in this section have been applied to the experimental determination of ki for a number of materials using the ESA 31 with high resolution. Results are presented in [177–181] and summarized in [183]. The method proved to be suitable for polymers too [224]. High-energy (<50 keV) ki results are presented in [13,225], including their Z dependence. The maxima of the IMFP values coincide with minima of density values for the elements. Thus, it would be more informative to express ki data in atomic layer units [175]. Another important problem is the role of surface excitation. Calculated ki data are based on the dielectric function of the solid, determined usually from optical data. The ki data are valid for the bulk of the solid. Kwei et al. defined a depth dependent inverse IMFP, produced by surface and volume excitations [11,192]. In Fig. 12, res ðEÞ spectra as measured by different RFA spectrometers are compared for Ag, together with MC simulations [107]. The differences between MC calculations and experiments begin at E < 200 eV. They are due to surface excitation, such as surface plasmons. Better agreement with experiment was found by Chen [108], after taking into consideration the surface excitations. In Fig. 27, the REELS spectra of GaSb exhibit a strong surface plasmon at E ¼ 0:2 keV. The intensity of this peak is reduced at E ¼ 2 keV. In the Fig. 32, res ðEÞ calculated data for Cu [108] are plotted versus ki for only bulk and bulk þ surface losses, respectively. The same res ðEÞ experimental results can be interpreted by assuming only bulk excitation in the MC simulations, or taking into consideration also surface excitation. They result in different ki values. Kwei et al. [11] introduced the SEP Ps for electrons crossing a solid surface. They present calculated SEP values for several elements and compounds. In Fig. 33, Ps ðEÞ and the depth ðxÞ dependence of 1=ki , and its decomposition to surface and volume excitations are presented for Ni, with E ¼ 800 eV incident electrons. Their sum is roughly constant. In Ni the average atomic distance is nearly 0.23 nm, i.e. the surface excitation is important within 1–2 ML. Fig. 33 refers to incident electrons. Similar effects occur with escaping electrons. In EPES surface excitation of incident þ escaping electrons is characterized by Pse . In conclusion the role of surface excitation is predominant for low E (E < 500 eV). Surface excitation correction is needed in EPES–IMFP experiments [181]: The calculated ratio of Iesc =Ierc should be corrected by Pses of the sample and Pser of the reference: Ies =Ier ¼ Iesc ð1  Pses Þ=Ierc ð1  Pser Þ

ð6:1Þ

Section 6.4 deals with experimental determination of SEP Ps . The IMFP can be deduced from REELS and Kki spectra, if reliable KðE; EL Þ values are available, based on optical data [6,189,228,229]. In a very recent work, Fuentes et al. [230] determined the IMFP of selected Ti compounds from the evaluation of REELS spectra. SEP was taken into consideration.

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Fig. 32. Comparison of calculated res ðEÞ data, assuming only bulk (þ) and bulk þ surface excitation ðÞ for the same ki values [108].

Fig. 33. The depth dependence of the inverse mean free path produced by surface 1=kis and by volume 1=kiv losses for E ¼ 800 eV with Ni. The Ps ðEÞ is plotted versus E on the upper curve for incident electrons [11].

Finally a very special problem of the IMFP is mentioned. Hopster et al. [137] verified experimentally the spin dependence of the IMFP with ferromagnets. They found a ratio nearly 1.2 for up to down polarized electrons with a 4ML Fe/Cu(1 0 0) thin film structure, at E ¼ 10–40 eV. They presented a theoretical explanation of their experimental results.

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6.3. Determination of the inelastic-scattering cross section of electrons Electron energy loss spectroscopy in reflection mode (REELS) combined with EPES supply the cross section for inelastic scattering of electrons. In our early work on the plasmon losses of Mo, REELS was made quantitative by using the elastic peak as a reference peak [226]. Tougaard and Chorkendorff [189] developed a quantitative procedure for determining KðE; EL Þki ðEÞ, the probability of energy loss EL per unit path length, i.e. the cross section for inelastic electron-scattering. It is based on REELS spectra compared with the elastic peak. Tougaard et al. published a number of papers on KðE; EL Þki ðEÞ for Al [189], for Si, Cu, Ag, Au, Ti, Pd [6], for GaAs [227], on Si and SiO2 [228] and ZrO2 [229]. Tougaard developed a simple procedure for evaluating Kki from REELS experiments [6], and published a simple formula for Kki [10]. The integral KðEp ; EL Þki ðEp Þ should be extended to the total loss spectrum, but Kki is strongly decreased for EL > 100 eV. For dominating plasmon losses, the limit is the first plasmon peak, such as for Si, Ge, Al, GaAs, SiO2 , ZrO2 and the III–V semiconductors [149,227–229]. A special case is the first ionization loss peak at ELi and in the ri cross section. It can be observed very well in the REELS spectra, as a slight kink in the IðEL Þ electron spectrum. In general its intensity is very low, <103 –105 Ie ðEp Þ. In practice it is measured in derivative mode: I 0 ðEÞ or I 00 ðEÞ. The data evaluation is rather difficult. The cross section for surface vibrations of O, H and CO adsorbed on W has been estimated. The rsv excitation cross section is in 1017 –1018 cm2 from comparison of the HREELS loss peak for vibration with the elastic peak [231] at low Ep energy. In that case, the interaction is restricted to one monolayer. These problems are discussed in the book of Ibach et al. [232]. 6.4. Determination of the surface excitation parameter Actually, only EPES offers possibility for experimental estimation of the SEP. Besides, the abundant literature on theoretical analysis of surface excitation processes, [4,150–153] summarizes the bibliography. Few works have been published on experiments. The pioneering work of Chen et al. [108] with MC simulation gave calculated values of resRFA ðEÞ for Ag. They found better agreement with experiments, than [107] based on bulk parameters. Tanuma et al. [233] estimated Pse ðEÞ for Ni by comparing the experimental integrated elastic peak Ie ðEp Þ with its calculated value Ic ðEp Þ: Ie ðEp Þ=Ic ðEp Þ ¼ 1  Pse ðEÞ

ð6:2Þ

Ie ðEp Þ and Ic ðEp Þ are needed in absolute (%) units. Very few electron spectrometers are suitable for such experiments [41,72]. The main problem is the uncertainty of the transmission Tr of the CMA of Goto [75]. NPL software, however, can be used to determine Tr for Auger spectrometers. Another possibility is given by interpretation of REELS spectra [234,235]. Yubero et al. calculated KðE; EL Þ spectra for surface and bulk excitations in Si and Fe for

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some energies. They found good agreement with experiments, but Pse ðEÞ was not deduced. Werner et al. [4,236] studied AREPES and ARREELS spectra on Si and Al for E ¼ 0:3–3:4 keV. They deduced Pse from the ratio of the surface plasmon/elastic peak area [149,236] and achieved good agreement with calculated values using the Eq. (4.4) from [4,153]. Another approach was developed in our laboratory [149,237–239]. It is based on KðE; EL Þki ðEÞ spectra deduced from REELS experiments [6,238,239]. The spectra for various incident energies are normalized by factors fn ðEÞ to have the same value at E ¼ Epl (bulk plasmon) energy, as displayed for Si in Fig. 34. Above E > Epl the curves for different energies nearly overlap. Surface excitation appears at the low energy E < Epl side of the spectrum. The bulk plasmon loss peak was approximated using TougaardÕs three parameter Lorentzian formula [10] shown in Fig. 35 for

Fig. 34. Normalised fn KðE; EL Þki ðEÞ inelastic-scattering cross sections of Si, fitted at E ¼ Epl1 bulk plasmon energy [148], plotted in arbitrary units.

Fig. 35. KðE ¼ 5 keV; EL Þki (5 keV) spectrum of Si. The bulk plasmon is approximated by TougaardÕs formula, indicated on the figure.

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Fig. 36. Ps ðEÞ SEP of Si and Ge, compared with calculated data [153,236]. Notations are indicated on the figure.

E ¼ 5 keV. The difference spectra from the normalized experimental KðE; EL Þki ðEÞ spectra and the Tougaard formula give the normalized surface plasmon loss peak intensity for each energy. By renormalization, Pse ðEÞ was estimated [148,237]. In Fig. 36, the experimental Pse ðEÞ results for Si and Ge are compared with those calculated with Eq. (4.4). The agreement is quite good. Our procedure is confined to materials characterized by dominant surface and bulk plasmon losses: semiconductors and some metals only [148]. For other type of materials, such as e.g. Ag and Fe, another approach has been developed in our laboratory [149]. It is based on reference standard samples: polySi (polycrystalline), aGe (amorphous) and Sn plasmon dominated loss spectra [239], developed in our laboratory. This work is in progress. Reliable Pse values are now available for polySi and aGe, whereas Pse is not known for Ni and Ag, used for reference samples. polySi and aGe are perspective reference samples for EPES. 6.5. Determination of the cross section for electron induced desorption (EID) Electron impact can produce desorption of some elements in a compound or at an adsorbed layer. Organic compounds containing hydrogen lose H following electron irradiation. The intensity Ie ðEp ; tÞ increases with time t. The phenomenon is illustrated on a Zn-phthalocyanine thin film in Fig. 37 during irradiation for t ¼ 60 s. The development of the elastic peak intensity Ie ðE; tÞ with t is displayed. It is affected by the H content of the sample, decreasing the intensity of elastic peak. The C–H bonds are broken by electron irradiation. Due to the desorption of H ; Ie ðE; tÞ increases with t. Jardin determined rEID from EPES measurements and resulted in 8  1018 cm2 for E ¼ 500 eV [31]. This is the order of magnitude of dissociative ionization cross section.

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Fig. 37. Variation of the elastic peak intensity for phthalocyanine with t during electron bombardment.

7. An outlook This monograph has summarized the main features, possibilities and problems of EPES. Since 1981 every year a growing number of papers have been published on its further development. Further development of instrumentation, spectrometers, their operating parameters, accuracy and performance is expected in the future. The same can be foreseen concerning the treatment of physical processes and evaluation procedures of experimental results using MC simulation or transport methods. Experimental determination and calculation of physical parameters of EPES, namely the IMFP, the differential and total elastic and inelastic-scattering cross sections, the lifetime of medium energy electrons [8], etc., will be continued. The applications of EPES in surface science will be extended. In the authorÕs view more work is needed on: • Improving the amorphization procedures of crystalline surface layers and their characterization [21–24]. • Revealing the effects of partial amorphization and surface roughness in EPES [16]. • Monte Carlo simulation of ordered and partially disordered systems. New software needs to be developed. • Improvement of spectrometer correction procedures [92] for analyzers of poor energy resolution (CMA, RFA) DEs . • Better reference standard materials for the measurement of the IMFP [17]. • Compilation of absolute values of the elastic reflection coefficient, including its angular dependence.

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• Experimental and theoretical research in the low energy (E < 200 eV) range. The IMFP and its depth dependence. Refraction effects. Surface excitation. • EPES using monoenergetic primary electrons, as used actually in HREELS, but confined to very low energies (E < 10 eV). Monochromatized electrons can be accelerated to higher energies for EPES experiments. No such work or instrument has been published as yet. • Further applications of EXFSEPES and SPEPES. • Application of EPES–REELS in electron microscopy and STM [14].

Acknowledgements The author expresses his sincere thanks and appreciation to a number of colleagues. At first this report contains many results of joint research at the Research Institute of Technical Physics and Materials Science of the Hungarian Academy of Sciences, Budapest with my colleagues: M. Menyhard, A. Sulyok, S. Gurban, A. Barna, T. Orosz, K. Pentek, A. Konkol, Zs. Benedek, Cs. Daroczi, Z. Csahok. Some of the work was done with my colleagues at the Nuclear Research Institute of the Hungarian Academy of Sciences, Debrecen: L. Toth, D. Varga, K. Toekesi, Z. Berenyi and L. Koever. Numerous joint studies were obtained in international cooperation with: A. Jablonski, B. Lesiak, M. Krawczyk, P. Mrozek, and A. Kosinski, at the Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw; with B. Gruzza, L. Bideux, C. Robert, A. Porte and P. Bondotþ , at the Universite Blaise-Pascal de Clermont-Ferrand; with C. Jardin and P. Michel, at the Universite Claude-Bernard de Lyon; with S. Tougaard, at the Physics Department of the University of Southern Denmark, Odense. The author acknowledges valuable discussions with: M. Menyhard, B. Gruzza, S. Tougaard, C. Jardin and C.J. Powell; and in particular with A. Jablonski. The author is grateful for receiving preprints and reprints from C.J. Powell (NIST), K. Goto (Nagoya Inst. Technol), S. Mroz (Univ.Wroclaw), W.S.M. Werner (TU Wien), H. Seilerþ (Univ. Hohenheim-Stuttgart), L. Reimer (Univ. Muenster), H. Gaukler (Univ. Tuebingen), Y.F. Chen, C.M. Kwei (Nat. Chiao Tung. Univ.), H. Hopster (Univ.California). M.P. Seah (NPL, Teddington). Author expresses his thanks to prof. K.Goto and to the Surface Analysis Soc. of Japan for kindly communicating the Ni reference data and to C.J. Powell to his kind permission for reproducing results from NIST database 64. The author expresses his gratitude to S. Gurban and T. Orosz for preparing the manuscript and to Mrs. S. Toth and G. Glaser for preparing the figures. The research program has been supported by the Research Institute for Technical Physics and Materials Sciences of the Hungarian Academy of Sciences, Budapest and its Director, Prof. J. Gyulai and the EU COPERNICUS program under ERBIC 15CT960800, OMFB KBN-TET PL-17/99 (Hungarian-Polish Cooperation Contract), Hung. Acad. Sci.-CNRS (France) Cooperation, OTKA (Hung. Nat. Res. Fund) TO30433 and T037709 Projects.

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