A method is proposed for easy determination of the mass thickness of thin films using electron-pmbe microanalysis. The model is based on the function of the depth distribution &z) of the characteristic x-ray production and emphasizes the treatment of the physical phenomena in the transition area between the film and the substrate. The method is applicable to a wide range of elements and element combinations (2 > 5 ) and electron acceleration energies. It has been tested by comparing results obtained using this method with data taken from the literature. Emrs are small, generally, not exceeding 5%.
The depth distribution function for characteristic x‐radiation is calculated using a simple electron scattering model, which quantifies the amount of electrons being scattered back and forth in the sample. The quantities used for the calculation are the transmission and backscattering coefficients, the corresponding energy and angular distributions and the ionization cross‐section. The physical background and implications of this model are discussed.
An analytical expression for the surface ionization @(O) is derived from fundamentals, viz., the ionization cross section and the angular and energy distribution of backscattered electrons. In order to avoid numerical integrations, a simple formula for the energy distribution of backscattered electrons is presented. The values given by the resulting expression for @(O) are compared with those given by already known formulae and with experimental findings. In general, the agreement is quite satisfactory, although the calculated values generally are smaller than those experimentally found, especially at high overvoltages. This can at least partly be explained by secondary fluorescence excited by the continuous radiation, of which the correction has not been taken into account in the experimental determination of the (P(0) values.
Several analytical expressions for the electron backscattering coefficient for massive homogeneous samples are compared with experimental data, directing special attention to the dependence of this quantity on the electron acceleration energy. It is shown that this dependence generally cannot be neglected. The expression proposed by Hunger and Küchler turns out to be better than that of Love and Scott, although even the better formula can be slightly improved by a small modification.
Three recently developed absorption and atomic number correction procedures have been investigated with regard to possible improvements and to the performance of these improved models, which has been studied depending on different values of the absorption correction factor. The test file includes 655 measurements of elements with Z > 10 and 258 B-, C-, and Nmeasurements. The results show that the models of Bastin and Heijligers and of Sewell, Love, and Scott generally are substantially better than the one of Tanuma and Nagashima or the established ZAF approach.
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