A comparison on absorption coefficients for secondary electron emission obtained from two different formulas

Abstract

In this work, the absorption coefficients for secondary electron emißsion, α and β, that appeared respectively in the two different formulas, \(\delta (E_p ) = k\int_0^\infty {\left( {\frac{{dE}}
{{dz}}} \right)E_p \exp ( - \alpha z)dz} \) and \(\delta (E_p ) = k\int_0^\infty {\left( {\frac{{dE}}
{{dz}}} \right)E_p \exp ( - \alpha z)dz} \), were derived with a standard deviation rate analysis method based on a Monte Carlo simulated secondary electron yield, δ(E_p). Both the energy dissipation in depth for primary electrons, \(\left( {dE/dz} \right)E_p \), and the depth distribution for the number of secondary electrons including cascade electrons, n(z, E_p), were obtained by the same Monte Carlo method, in which the discrete inelastic scattering model was employed. The calculation results for Cu and Mg show that the n(z, E_p)-curve differs significantly from the \(\left( {dE/dz} \right)E_p \)-curve, and thus as well as a from b, for varied incidence angles (0°–80°) and low-energy primary electrons (up to 3 keV). The absorption coefficient β-values derived from a realistic depth distribution of cascade secondary electrons, n(z, E_p), then describe more accurately the nature of attenuation behavior of secondary electrons than a-values that associated with the approximate formula.