Transport Equation Approach to Electron Microbeam Analysis: Fundamentals and Applications

The sensitivity of backscattering coefficients to elastic scattering cross‐sections and electron stopping powers

“…The work of Tilinin and Werner (Tilinin and Werner, ; Werner, ) emphasizes how the backscattering coefficient η can to a reasonable approximation be expressed as a function of the scattering parameter ξ evaluated at the incident electron primary energy. This is achieved because ξ is relatively insensitive to primary energy over the energy range in which electrons contribute most to η .…”

“…The way in which Δ η / η varies with energy depends on how η varies with ξ ( E p ) and, without going into fine detail, it is possible to get some insight into the atomic number dependence of these quantities. The calculations of Tinin and Werner (Tilinin and Werner, ; Werner, ) suggest that for higher atomic number systems such as Ag and Au ξ decreases slowly with energy between 1,000 and 10,000 eV resulting in a relatively low and almost constant value of Δ η / η . Below 1,000 eV λ tr for high atomic number systems tends to increase rapidly essentially due to a partial Ramsauer Townsend Effect (Cumpson, ; Matthew et al ., ) involving interference in scattering amplitudes due to multiple scattering within the atom.…”

“…There are measurement difficulties due to surface contamination (few studies have been done under ultra high vacuum conditions (Joy, ; Bronstein and Fraiman, ; El‐Gomati et al ., ; Joy Database ), due to the need for estimates of secondary electron contributions to the signal and due to variation of detector sensitivity with electron energy. On the theoretical side there are two approaches: quasi analytic transport theories (Tilinin and Werner, ; Werner, ) and Monte Carlo simulations (Joy, ; Demers and Gauvin, ; Salvat et al ., ). In both cases the results depend on the accuracy of the inputs of both elastic and inelastic scattering data.…”

“…In balancing the relative effects of elastic and inelastic scattering the scattering parameter ξ = R 0 / λ tr (see Tilinin and Werner, ; Werner, ), has proved useful and we will employ ξ to gain insights into the Monte Carlo approach. It is not the objective of this work to compare theory and experiment directly, but rather to examine the sensitivity of predictions of η to changes in the two key parameters, the differential elastic scattering cross‐section d σ /dΩ and the stopping power S ( E ), that control the phenomenon within the continuous slowing down approximation.…”