Angular distribution of electrons reflected elastically from noncrystalline solid surfaces

Surface & Interface Analysis

2005

The inelastic mean free path (IMFP) of electrons in solids is an important parameter needed for quantitative applications of electron spectroscopies: X-ray photoelectron spectroscopy and Auger electron spectroscopy (AES). The IMFP values published for compounds or alloys are rather limited, and in general case, the predictive formulas must be used. Unfortunately, accuracy of these formulas may be rather low in some cases. There is an obvious need for a simple method that conveniently provides the IMFP values for a studied solid. Such conditions are satisfied by the method that makes it possible to derive the IMFP values from the measured elastic backscattering probability. The present report contains a concise introduction to this method; the main features of such an approach are briefly reviewed and discussed. The method, with some caution, can be applied to any solid, although the conducting or the semiconductor samples are recommended to avoid charging effects. In contrast with the method involving deposition of overlayers, the IMFP values derived from the elastic backscattering intensity are in agreement with the definition supported by American Society for Testing and Materials (ASTM). The measurements can be made using typical electron spectrometers in situ for samples submitted to other studies. Finally, the measurements are nondestructive. The main problem of this method is the complexity of the theoretical model describing multiple electron scattering events in the solid. To facilitate calculations, an extensive user-friendly software packet, EPES has been developed. One of the functions of this packet is to determine, from the Monte Carlo (MC) simulations, the so-called calibration curve, i.e. the dependence of the backscattering probability on the input value of the IMFP. Calculations can be performed for any experimental configuration, and for electron energies ranging from 50 to 10 000 eV. The theoretical model requires knowledge of the total and differential elastic scattering cross sections (DCS). These parameters can be imported from all versions of the NIST Database 64.

Section: Introductionmentioning

confidence: 99%

“…Typically, this number does not exceed 10 7 . As mentioned, the formalism outlined above refers to the elemental solids.…”

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confidence: 97%

Determination of the electron inelastic mean free path in solids from the elastic electron backscattering intensity

Surface & Interface Analysis

2005

“…In effect, more than one or two elastic collisions have to be described accurately. We may expect that the formalism of Werner et al 24 suffers from the same problem, and has limited applicability at high electron energies.…”

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confidence: 96%

“…The resulting angular distribution of electrons is introduced as a source function to the Boltzmann equation. The formalism derived by Werner et al 24 is very complex, which may create problems for practical use. Furthermore, its reliability has not been analysed in detail.…”

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confidence: 99%

“…To the author's knowledge, the only source of IMFPs obtained from a more realistic analytical theory has been published by Beischmidt et al 23 Details of the theory were published separately by Werner et al 24 The relation between elastic backscattering probability and the IMFP has been derived from an approximate solution of the Boltzmann equation within the so-called transport approximation. A similar approach published earlier by Dwyer, 9 however, has not been used for the determination of the IMFPs.…”

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confidence: 99%

See 1 more Smart Citation

Determination of the IMFP from electron elastic backscattering probability

2000

Surf. Interface Anal.

Theoretical models for elastic electron backscattering from surfaces have gained much attention in the recent years. One of the stimulating factors is the need for a reliable theoretical relation between the elastic backscattering probability and the electron inelastic mean free path (IMFP) in the surface region. Such a relation would provide a convenient tool for determining the IMFP. At present, the Monte Carlo simulations are considered to be most reliable for a description of elastic electron backscattering. This approach, however, usually needs considerable computing time. The analytical theoretical models are derived after introducing additional simplifying assumptions that may lead to a certain systematic deviation with respect to the Monte Carlo simulations. In the present work, a modification of the theoretical model proposed by Oswald, Kasper and Gaukler (OKG) is compared with Monte Carlo simulations. Calculations were made for the most frequently used experimental geometry (cylindrical mirror analyses with normal incidence of the primary beam) and a wide range of energies and atomic numbers. It has been found that the elastic backscattering probabilities calculated from the OKG model and the Monte Carlo model compare very well if we assume realistic values of the IMFP. For this reason, the OKG model is recommended for calculations associated with determination of the IMFP when the experimental geometry similar to that of the CMA is used. Copyright © 2000 John Wiley & Sons, Ltd.

Elastic Electron Backscattering from Surfaces at Low Energies

Jiřı́ček

1996

Surf. Interface Anal.

A novel experimental method, involving reverse‐view LEED optics, is proposed for simultaneous determination of the angular distribution of elastically backscattered electrons and the energy dependence of elastically backscattered intensity. Extensive measurements in the energy range 50–500 eV were performed for Al, Cu, Pt and Au. The experimental energy and angular dependences of the backscattered intensity were found to compare very well with results of Monte Carlo simulations performed in the energy range considered. This indicates that the procedure of determining the inelastic mean free path from the elastically backscattered intensities can also be used in the low electron energy region. The performance of theory is somewhat worse in the case of aluminium, and thus the use of this metal as standard is not recommended.