The energy dependence of a diffusion model for an electron probe into solid targets

The penetration and energy loss characteristics of an electron probe with energies 1 and 103 keV in solid targets are analysed by using the potential function of the power and exponential forms of the potential function with a screened atomic radius for scatterings. Then, the diffusion effect due to multiple collisions is combined with the energy retardation in accordance with a modified Thomson-Whiddington law, with the scattering cross-section in the Lenard absorption law, to give consistent expressions for the variation of the transmission fraction etaT and back-scattering fraction etaB with depth y = x/R together with the diffusion depth yD and the maximum energy loss depth yE normalised by the penetration range R as a function of the parameter γ (which is a function of the incident energy and the atomic number). Diffusion is considered to take place through a hemisphere with a centre located at the most probable energy dissipation depth yC, related to the diffusion depth yD. The maximum dissipation depth yE is found to agree well with experiment, leading to a quantitative analysis of the penetration and energy retardation of an electron probe in scanning electron microscopy. (author)